You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:

Question

A coil has $N$ turns and current passes through it is $I$ ampere then we obtain $L$ of self inductance. Now if current is made doubled then new self inductance be ______ H.

Answer 1

To ascertain the quantity of turns in the solenoid, the inductance $ L $ formula is utilized:

L = \frac{μ N_{2} A}{l}

Where:

$L$ represents inductance (0.016 H)
$μ$ denotes permeability of free space ($4π \times 10^{-7} \, \text{Tm/A}$)
$N$ is the number of turns
$A$ is the cross-sectional area
$l$ is the solenoid's length (0.81 m)

The solenoid's cross-sectional area $ A $ is calculated as:

A = πr r^{2}

Given a radius $ r = 0.02 \, \text{m} $, the area is computed:

A = π (</mo>0.02)^{2}

Substituting values to find $ A $:

= 3.1416 \times (</mo>0.02)^{2}=1.25664\times10-3 m2

Inserting this into the inductance formula yields:

0.016 = (</mo>4π\times10-7)N^{2}(</mo>1.25664\times10-3)0.81Rearranging to solve for \( N^2 \):N N^{2} = \frac{0.016}{\frac{0.81}{(</mo>4π\times10-7)}} \div (</mo>1.25664\times10-3)Finally, solving for \( N \):N = \sqrt{\frac{0.016}{\frac{0.81}{(</mo>4π\times10-7)}} \div (</mo>1.25664\times10-3)}The computed number of turns is approximately \( N \approx 2976 \).Download Solution in PDFWas this answer helpful? 4Top Questions on  Electromagnetic induction A coil has $N$ turns and current passes through it is $I$ ampere then we obtain $L$ of self inductance. Now if current is made doubled then new self inductance be ______ H. GUJCET - 2026 Physics Electromagnetic induction View Solution The dimensional formula of $\frac{B^2}{2\mu_0}$ is ______. GUJCET - 2026 Physics Electromagnetic induction View Solution Two concentric circular coils, one of small radius $r_1$ and the other of large radius $r_2$, such that $r_1 \ll r_2$, are placed co-axially with centres coinciding. The mutual inductance $M$ of the arrangement is proportional to ______. GUJCET - 2026 Physics Electromagnetic induction View Solution A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ___ mV. JEE Main - 2026 Physics Electromagnetic induction View Solution Want to practice more? Try solving extra ecology questions today View All Questions Questions Asked in CBSE Class XII exam Monascus purpureus is a yeast used commercially in the production of which one of the following? CBSE Class XII - 2026 Microbiology View Solution The foetal ejection reflex in human triggers the release of _______ hormone from _______CBSE Class XII - 2026 General Physiology View Solution A DNA molecule is 160 base pairs long. It has 30% Guanine. How many Adenine bases are present in this DNA molecule? CBSE Class XII - 2026 Genetics View Solution Look at the given image and identify the ancient sculptural panel from the options: | CBSE Class XII - 2026 Ancient History View Solution Arrange the following historical events in chronological order and choose the correct option:

I. Champaran Satyagraha II. Kheda Satyagraha III. Jallianwala Bagh Incident IV. Rowlatt Act Options: CBSE Class XII - 2026 Modern Indian History View Solutioncontact us terms & conditions Privacy & Policy © 2026 Patronum Web Private Limited{"props":{"isServer":true,"initialState":{"globalData":{"dropdown":{"explore":{}},"isMobile":false,"asPath":"/exams/questions/you-are-required-to-design-an-air-filled-solenoid-67bf0695abfe1fd1609cb58c"},"userData":{},"authentication":{"token":null},"hashHandler":{"name":"customHashes","states":[]},"leadData":{},"leadFormStatus":{"formType":"Lead","visibility":"initial","mandate":false,"sourceInfo":{"source":null,"fields":{}},"fromPopup":false,"leadformData":{}},"leadFormParams":{"leadParamsData":{}},"popupStatus":{"status":"close","popupType":"null","lastPopupType":"null","popupData":{}},"pagenameData":{"name":"exam_question"},"qnaData":{"data":{}},"reviewAuthData":{"type":"getOTP","data":{},"signupJson":{},"activeSearchTab":"india","isReviewAuth":false},"revisitData":{},"adsData":{"page":"","micrositeAdBlock":0,"ssrComplete":false},"collegePageBdData":{"breadcrumb":[]},"loaderData":{"isLoading":false,"isDataFetching":false},"rankPredictorData":{"formData":{}},"footerFieldData":{"data":{}},"appliedColleges":{"applied":[],"shortlisted":[]},"referralData":{}},"initialProps":{"pageProps":{"pageName":"exam_question","importantLinks":[],"examInfo":{},"pageData":{"questionBySlug":{"id":"67bf0695abfe1fd1609cb58c","text":{"default":"\u003cdiv\u003e\u003cstrong\u003eYou are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:\u003c/strong\u003e\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"you-are-required-to-design-an-air-filled-solenoid-67bf0695abfe1fd1609cb58c","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2025","year":2025,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ","updatedAt":"2026-02-19T02:25:55.420Z","createdAt":"2025-02-26T12:18:32.082Z","hint":{"default":"\u003cdiv\u003eFor air-filled solenoids, permeability \\( \\mu_r = 1 \\). Always check the unit consistency when using formulas.\u003c/div\u003e","__typename":"LanguageField"},"difficulty":"MEDIUM","solution":{"text":{"default":"\u003cdiv\u003eTo ascertain the quantity of turns in the solenoid, the inductance \\( L \\) formula is utilized:\u003c/div\u003e\u003cdiv style=\"margin-top:10px;\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eL\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmfrac\u003e\u003cmrow\u003e\u003cmi\u003eμ\u003c/mi\u003e\u003cmsub\u003e\u003cmi\u003eN\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msub\u003e\u003cmi\u003eA\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow\u003e\u003cmi\u003el\u003c/mi\u003e\u003c/mrow\u003e\u003c/mfrac\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv\u003eWhere:\u003c/div\u003e\u003cul\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eL\u003c/mi\u003e\u003c/math\u003e represents inductance (0.016 H)\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eμ\u003c/mi\u003e\u003c/math\u003e denotes permeability of free space (\\(4π \\times 10^{-7} \\, \\text{Tm/A}\\))\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eN\u003c/mi\u003e\u003c/math\u003e is the number of turns\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eA\u003c/mi\u003e\u003c/math\u003e is the cross-sectional area\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003el\u003c/mi\u003e\u003c/math\u003e is the solenoid's length (0.81 m)\u003c/li\u003e\u003c/ul\u003e\u003cdiv\u003eThe solenoid's cross-sectional area \\( A \\) is calculated as:\u003c/div\u003e\u003cdiv style=\"margin-top:10px;\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eA\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eπr\u003c/mi\u003e\u003cmsup\u003e\u003cmi\u003er\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv\u003eGiven a radius \\( r = 0.02 \\, \\text{m} \\), the area is computed:\u003c/div\u003e\u003cdiv style=\"margin-top:10px;\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eA\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eπ\u003c/mi\u003e\u003cmo\u003e(\u0026lt;/mo\u003e\u003cmn\u003e0.02\u003c/mn\u003e\u003cmsup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv\u003eSubstituting values to find \\( A \\):\u003c/div\u003e\u003cdiv style=\"margin-top:10px;\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e3.1416\u003c/mn\u003e\u003cmo\u003e\times\u003c/mo\u003e\u003cmo\u003e(\u0026lt;/mo\u003e\u003cmn\u003e0.02\u003c/mn\u003e\u003cmsup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1.25664\u003c/mn\u003e\u003cmo\u003e\times\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmsup\u003e\u003cmn\u003e-3\u003c/mn\u003e\u003c/msup\u003e\u003c/mrow\u003e \u003cmo\u003em\u003csup\u003e2\u003c/sup\u003e\u003c/mo\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv\u003eInserting this into the inductance formula yields:\u003c/div\u003e\u003cdiv style=\"margin-top:10px;\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003e0.016\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmfrac\u003e\u003cmrow\u003e\u003cmo\u003e(\u0026lt;/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmi\u003eπ\u003c/mi\u003e\u003cmn\u003e\times10\u003c/mn\u003e\u003cmsup\u003e\u003cmn\u003e-7\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmsup\u003e\u003cmi\u003eN\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e(\u0026lt;/mo\u003e\u003cmn\u003e1.25664\u003c/mn\u003e\u003cmo\u003e\times\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmsup\u003e\u003cmn\u003e-3\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmrow\u003e\u003cmn\u003e0.81\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfrac\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv\u003eRearranging to solve for \\( N^2 \\):\u003c/div\u003e\u003cdiv style=\"margin-top:10px;\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eN\u003c/mi\u003e\u003cmsup\u003e\u003cmi\u003eN\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmfrac\u003e\u003cmn\u003e0.016\u003c/mn\u003e\u003cmfrac\u003e\u003cmn\u003e0.81\u003c/mn\u003e\u003cmo\u003e(\u0026lt;/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmi\u003eπ\u003c/mi\u003e\u003cmn\u003e\times10\u003c/mn\u003e\u003cmsup\u003e\u003cmn\u003e-7\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mfrac\u003e\u003c/mfrac\u003e\u003cmo\u003e\div\u003c/mo\u003e\u003cmo\u003e(\u0026lt;/mo\u003e\u003cmn\u003e1.25664\u003c/mn\u003e\u003cmo\u003e\times\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmsup\u003e\u003cmn\u003e-3\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv\u003eFinally, solving for \\( N \\):\u003c/div\u003e\u003cdiv style=\"margin-top:10px;\"\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eN\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsqrt\u003e\u003cmfrac\u003e\u003cmn\u003e0.016\u003c/mn\u003e\u003cmfrac\u003e\u003cmn\u003e0.81\u003c/mn\u003e\u003cmo\u003e(\u0026lt;/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmi\u003eπ\u003c/mi\u003e\u003cmn\u003e\times10\u003c/mn\u003e\u003cmsup\u003e\u003cmn\u003e-7\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mfrac\u003e\u003c/mfrac\u003e\u003cmo\u003e\div\u003c/mo\u003e\u003cmo\u003e(\u0026lt;/mo\u003e\u003cmn\u003e1.25664\u003c/mn\u003e\u003cmo\u003e\times\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmsup\u003e\u003cmn\u003e-3\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/msqrt\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv\u003eThe computed number of turns is approximately \\( N \\approx 2976 \\).\u003c/div\u003e","__typename":"LanguageField"},"concepts":[],"formulas":[],"expert":null,"__typename":"QuestionSolution"},"otherSolutions":[],"externalVideos":[],"stats":{"likes":4,"dislikes":5,"__typename":"QuestionStats"},"options":[{"content":{"default":"\u003cdiv\u003e2592 \u003cbr\u003e\u003c/div\u003e","__typename":"LanguageField"},"isCorrect":false,"__typename":"QuestionOption"},{"content":{"default":"\u003cdiv\u003e2866 \u003cbr\u003e\u003c/div\u003e","__typename":"LanguageField"},"isCorrect":false,"__typename":"QuestionOption"},{"content":{"default":"\u003cdiv\u003e2976 \u003cbr\u003e\u003c/div\u003e","__typename":"LanguageField"},"isCorrect":true,"__typename":"QuestionOption"},{"content":{"default":"\u003cdiv\u003e3140 \u003cbr\u003e\u003c/div\u003e","__typename":"LanguageField"},"isCorrect":false,"__typename":"QuestionOption"}],"seo":{"title":"You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. 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Now if current is made doubled then new self inductance be ______ H.\u003c/strong\u003e \u003cbr\u003e\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"a-coil-has-n-turns-and-current-passes-through-it-i-69c92bd2cafec0c6cf7ea463","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"GUJCET","__typename":"LanguageField"},"externalExamId":563,"tagName":"GUJCET - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"69c92bd2cafec0c6cf7ea460","text":{"default":"\u003cdiv\u003e\u003cstrong\u003eThe dimensional formula of $\\frac{B^2}{2\\mu_0}$ is ______.\u003c/strong\u003e\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"the-dimensional-formula-of-frac-b-2-2-mu-0-is-69c92bd2cafec0c6cf7ea460","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"GUJCET","__typename":"LanguageField"},"externalExamId":563,"tagName":"GUJCET - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"69c92bd2cafec0c6cf7ea45c","text":{"default":"\u003cdiv\u003e\u003cstrong\u003eTwo concentric circular coils, one of small radius $r_1$ and the other of large radius $r_2$, such that $r_1 \\ll r_2$, are placed co-axially with centres coinciding. The mutual inductance $M$ of the arrangement is proportional to ______.\u003c/strong\u003e \u003cbr\u003e\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"two-concentric-circular-coils-one-of-small-radius-69c92bd2cafec0c6cf7ea45c","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"GUJCET","__typename":"LanguageField"},"externalExamId":563,"tagName":"GUJCET - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"69842cf86ad5ecb7befc9845","text":{"default":"\u003cdiv\u003eA circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ___ mV. \u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"a-circular-loop-of-radius-7-cm-is-placed-in-unifor-69842cf86ad5ecb7befc9845","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"JEE Main","__typename":"LanguageField"},"externalExamId":301,"tagName":"JEE Main - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"698362300da5bbe78f022785","text":{"default":"\u003cdiv\u003eA spherical body of radius $r$ and density $\\sigma$ falls freely through a viscous liquid having density $\\rho$ and viscosity $\\eta$ and attains a terminal velocity $v_0$. Estimated maximum error in the quantity $\\eta$ is : (Ignore errors associated with $\\sigma$, $\\rho$ and $g$, gravitational acceleration) \u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"a-spherical-body-of-radius-r-and-density-sigma-fal-698362300da5bbe78f022785","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"JEE Main","__typename":"LanguageField"},"externalExamId":301,"tagName":"JEE Main - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"6983622f0da5bbe78f02263d","text":{"default":"\u003cdiv\u003eIf \\(\\varepsilon_0\\), \\(E\\) and \\(t\\) represent the free space permittivity, electric field and time respectively, then the unit of\n\\[\n\\frac{\\varepsilon_0 E}{t}\n\\]\nwill be\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"if-varepsilon-0-e-and-t-represent-the-free-space-p-6983622f0da5bbe78f02263d","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"JEE Main","__typename":"LanguageField"},"externalExamId":301,"tagName":"JEE Main - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"6972538fa53643c511a42269","text":{"default":"\u003cdiv\u003e\u003cstrong\u003eA rod of mass \\(m\\) and length \\(L\\) is released on a rail placed in a uniform magnetic field \\(B\\) as shown. The circuit has resistance \\(R\\). What will be the terminal velocity of the rod?\u003c/strong\u003e\n\nv\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"a-rod-of-mass-m-and-length-l-is-released-on-a-rail-6972538fa53643c511a42269","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"JEE Main","__typename":"LanguageField"},"externalExamId":301,"tagName":"JEE Main - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"6983622f0da5bbe78f022610","text":{"default":"\u003cdiv\u003eFigure shows the circuit that contains three resistances (\\(9\\,\\Omega\\) each) and two inductors (\\(4\\,\\text{mH}\\) each). The reading of ammeter at the moment switch \\(K\\) is turned ON, is _________ A.\n\n    \u003cfigure class=\"image\"\u003e\u003cimg data-src-id=\"69835a3d0da5bbe78fffa0e3\" src=\"https://images.collegedunia.com/public/qa/images/content/2026_02_04/image_57175cbe1770215997023.png\"\u003e\u003c/figure\u003e\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"figure-shows-the-circuit-that-contains-three-resis-6983622f0da5bbe78f022610","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"JEE Main","__typename":"LanguageField"},"externalExamId":301,"tagName":"JEE Main - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"6998fa8bed97f56ad36d4459","text":{"default":"\u003cdiv\u003eA square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"a-square-loop-of-side-0-50-m-is-placed-in-a-unifor-6998fa8bed97f56ad36d4459","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"6998fa8aed97f56ad36d4340","text":{"default":"\u003cdiv\u003eAssertion : Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more.  \n\nReason (R): Induced emf produced is directly proportional to the magnetic flux.\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"assertion-induced-emf-produced-in-a-coil-will-be-m-6998fa8aed97f56ad36d4340","subject":{"name":{"default":"Physics","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Electromagnetic induction","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"}],"examRelatedQuestions":[{"id":"69c88ddb5ce02d038aa07cbe","text":{"default":"\u003cdiv\u003e\u003cstrong\u003eMonascus purpureus is a yeast used commercially in the production of which one of the following?\u003c/strong\u003e\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"monascus-purpureus-is-a-yeast-used-commercially-in-69c88ddb5ce02d038aa07cbe","subject":{"name":{"default":"Biology ","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Microbiology","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"69c88ddb5ce02d038aa07cab","text":{"default":"\u003cdiv\u003e\u003cstrong\u003eThe foetal ejection reflex in human triggers the release of _______ hormone from _______\u003c/strong\u003e\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"the-foetal-ejection-reflex-in-human-triggers-the-r-69c88ddb5ce02d038aa07cab","subject":{"name":{"default":"Biology ","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"General Physiology","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"69c88ddb5ce02d038aa07cae","text":{"default":"\u003cdiv\u003e\u003cstrong\u003eA DNA molecule is 160 base pairs long. It has 30% Guanine. How many Adenine bases are present in this DNA molecule?\u003c/strong\u003e\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"a-dna-molecule-is-160-base-pairs-long-it-has-30-gu-69c88ddb5ce02d038aa07cae","subject":{"name":{"default":"Biology ","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Genetics","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"69ccc7ec7a7046e36e4a27b8","text":{"default":"\u003cp\u003eLook at the given image and identify the ancient sculptural panel from the options: \u0026nbsp;\u003cbr\u003e\u003cbr\u003e|\u003cimg data-src-id=\"69ccdd6ec190e5d69717bd75\" src=\"https://images.collegedunia.com/public/qa/images/content/2026_04_01/a_do_for_t_a6a8d47d1775033710574.jpeg\"\u003e\u003c/p\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"look-at-the-given-image-and-identify-the-ancient-s-69ccc7ec7a7046e36e4a27b8","subject":{"name":{"default":"History","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Ancient History","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"69ccc7ec7a7046e36e4a27d4","text":{"default":"\u003cdiv\u003eArrange the following historical events in chronological order and choose the correct option:\n\nI. Champaran Satyagraha \u003cbr\u003e\nII. Kheda Satyagraha \u003cbr\u003e\nIII. Jallianwala Bagh Incident \u003cbr\u003e\nIV. Rowlatt Act \u003cbr\u003e\n\nOptions:\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SINGLE_ANSWER_MCQ","slug":"arrange-the-following-historical-events-in-chronol-69ccc7ec7a7046e36e4a27d4","subject":{"name":{"default":"History","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Modern Indian History","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SingleAnswerMCQ"},{"id":"69ccc7ec7a7046e36e4a2840","text":{"default":"\u003cdiv\u003eName any two centres of Indian National Movement.\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SUBJECTIVE_QUESTION","slug":"name-any-two-centres-of-indian-national-movement-69ccc7ec7a7046e36e4a2840","subject":{"name":{"default":"History","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Modern Indian History","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SubjectiveQuestion"},{"id":"69ccc7ec7a7046e36e4a283d","text":{"default":"\u003cdiv\u003eMention any one medieval town.\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SUBJECTIVE_QUESTION","slug":"mention-any-one-medieval-town-69ccc7ec7a7046e36e4a283d","subject":{"name":{"default":"History","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Modern Indian History","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SubjectiveQuestion"},{"id":"69ccc7ec7a7046e36e4a283a","text":{"default":"\u003cdiv\u003eName any one town which was under the rule of Babur.\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SUBJECTIVE_QUESTION","slug":"name-any-one-town-which-was-under-the-rule-of-babu-69ccc7ec7a7046e36e4a283a","subject":{"name":{"default":"History","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Modern Indian History","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SubjectiveQuestion"},{"id":"69ccc7ec7a7046e36e4a2837","text":{"default":"\u003cdiv\u003eMention any one Harappan site from the present state of Haryana.\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SUBJECTIVE_QUESTION","slug":"mention-any-one-harappan-site-from-the-present-sta-69ccc7ec7a7046e36e4a2837","subject":{"name":{"default":"History","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Travellers of Medieval India","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SubjectiveQuestion"},{"id":"69ccc7ec7a7046e36e4a2834","text":{"default":"\u003cdiv\u003eOn the same political map of India, two places have been marked as A and B as the centres of Indian National Movement. Identify them and write their correct name on the line drawn near them.\n\n\u003c/div\u003e","__typename":"LanguageField"},"type":"SUBJECTIVE_QUESTION","slug":"on-the-same-political-map-of-india-two-places-have-69ccc7ec7a7046e36e4a2834","subject":{"name":{"default":"History","__typename":"LanguageField"},"__typename":"Subject"},"topic":{"name":{"default":"Travellers of Medieval India","__typename":"LanguageField"},"__typename":"Topic"},"subtopics":[],"exams":[{"shortName":{"default":"CBSE Class XII","__typename":"LanguageField"},"externalExamId":704,"tagName":"CBSE Class XII - 2026","year":2026,"__typename":"Exam"}],"__typename":"SubjectiveQuestion"}],"parent":null}},"errorCode":false,"quesId":"67bf0695abfe1fd1609cb58c","examShortForm":"CBSE Class XII","schemaJsonLd":{"0":"{\"@context\":\"https://schema.org\",\"@type\":\"WebPage\",\"breadcrumb\":{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://questions.zollege.in/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Exams\",\"item\":\"https://questions.zollege.in//exams\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Physics\",\"item\":\"https://questions.zollege.in/exams/physics-questions\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Electromagnetic induction\",\"item\":\"https://questions.zollege.in/exams/physics-questions?topicIds=\"},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:\"}]}}","1":"{\"@context\":\"https://schema.org/\",\"@type\":\"QAPage\",\"name\":\"You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:\",\"description\":\"To ascertain the quantity of turns in the solenoid, the inductance \\\\( L \\\\) formula is utilized:L=μN2AlWhere:L represents inductance (0.016 H)μ denotes permeability of free space (\\\\(4π \\\\times 10^{-7} \\\\, \\\\text{Tm/A}\\\\))N is the number of turnsA is the cross-sectional areal is the solenoid's length (0.81 m)The solenoid's cross-sectional area \\\\( A \\\\) is calculated as:A=πrr2Given a radius \\\\( r = 0.02 \\\\, \\\\text{m} \\\\), the area is computed:A=π(\u0026lt;/mo\u003e0.02)2Substituting values to find \\\\( A \\\\):=3.1416\times(\u0026lt;/mo\u003e0.02)2=1.25664\times10-3 m2Inserting this into the inductance formula yields:0.016=(\u0026lt;/mo\u003e4π\times10-7)N2(\u0026lt;/mo\u003e1.25664\times10-3)0.81Rearranging to solve for \\\\( N^2 \\\\):NN2=0.0160.81(\u0026lt;/mo\u003e4π\times10-7)\div(\u0026lt;/mo\u003e1.25664\times10-3)Finally, solving for \\\\( N \\\\):N=0.0160.81(\u0026lt;/mo\u003e4π\times10-7)\div(\u0026lt;/mo\u003e1.25664\times10-3)The computed number of turns is approximately \\\\( N \\\\approx 2976 \\\\).\",\"url\":\"https://questions.zollege.in/exams/questions/you-are-required-to-design-an-air-filled-solenoid-67bf0695abfe1fd1609cb58c\",\"mainEntity\":{\"@type\":\"Question\",\"@id\":\"https://questions.zollege.in/exams/questions/you-are-required-to-design-an-air-filled-solenoid-67bf0695abfe1fd1609cb58c\",\"name\":\"You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:\",\"text\":\"You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:\",\"dateCreated\":\"2025-02-26T12:18:32.082Z\",\"datePublished\":\"2025-02-26T12:18:32.082Z\",\"dateModified\":\"2026-02-19T02:25:55.420Z\",\"answerCount\":\"1\",\"author\":{\"@type\":\"Person\",\"name\":\"questions.zollege.in Admin\"},\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\u003cdiv\u003e2976 \u003cbr\u003e\u003c/div\u003e\",\"upvoteCount\":4,\"url\":\"https://questions.zollege.in/exams/questions/you-are-required-to-design-an-air-filled-solenoid-67bf0695abfe1fd1609cb58c#solution\",\"author\":{\"@type\":\"Person\",\"name\":\"questions.zollege.in Admin\"},\"dateCreated\":\"2025-02-26T12:18:32.082Z\",\"datePublished\":\"2025-02-26T12:18:32.082Z\",\"dateModified\":\"2026-02-19T02:25:55.420Z\"},\"suggestedAnswer\":[]}}","2":"{\"@context\":\"https://schema.org/\",\"@type\":\"Quiz\",\"dateCreated\":\"2025-02-26T12:18:32.082Z\",\"dateModified\":\"2026-02-19T02:25:55.420Z\",\"typicalAgeRange\":\"11-18\",\"educationalLevel\":\"CBSE Class XII\",\"assesses\":\"Physics - Electromagnetic induction\",\"educationalAlignment\":[{\"@type\":\"AlignmentObject\",\"alignmentType\":\"educationalTopic\",\"targetName\":\"Electromagnetic induction\"},{\"@type\":\"AlignmentObject\",\"alignmentType\":\"educationalSubject\",\"targetName\":\"Physics\"},{\"@type\":\"AlignmentObject\",\"alignmentType\":\"educationalExam\",\"targetName\":\"CBSE Class XII\"}],\"name\":\"Quiz about Electromagnetic induction\",\"about\":{\"@type\":\"Thing\",\"name\":\"Physics - Electromagnetic induction\"},\"hasPart\":[{\"@type\":\"Question\",\"eduQuestionType\":\"Multiple choice\",\"learningResourceType\":\"Practice problem\",\"educationalLevel\":\"intermediate\",\"name\":\"Question About Electromagnetic induction\",\"text\":\"You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:}\",\"encodingFormat\":\"text/markdown\",\"comment\":{\"@type\":\"Comment\",\"text\":\"For air-filled solenoids, permeability \\\\( \\\\mu_r = 1 \\\\). Always check the unit consistency when using formulas.\"},\"suggestedAnswer\":[{\"@type\":\"Answer\",\"position\":0,\"encodingFormat\":\"text/markdown\",\"text\":\"\u003cdiv\u003e2592 \u003cbr\u003e\u003c/div\u003e\",\"comment\":{\"@type\":\"Comment\",\"text\":\"\\\"\\\"\"}},{\"@type\":\"Answer\",\"position\":1,\"encodingFormat\":\"text/markdown\",\"text\":\"\u003cdiv\u003e2866 \u003cbr\u003e\u003c/div\u003e\",\"comment\":{\"@type\":\"Comment\",\"text\":\"\\\"\\\"\"}},{\"@type\":\"Answer\",\"position\":2,\"encodingFormat\":\"text/markdown\",\"text\":\"\u003cdiv\u003e2976 \u003cbr\u003e\u003c/div\u003e\",\"comment\":{\"@type\":\"Comment\",\"text\":\"\\\"\\\"\"}},{\"@type\":\"Answer\",\"position\":3,\"encodingFormat\":\"text/markdown\",\"text\":\"\u003cdiv\u003e3140 \u003cbr\u003e\u003c/div\u003e\",\"comment\":{\"@type\":\"Comment\",\"text\":\"\\\"\\\"\"}}],\"acceptedAnswer\":{\"@type\":\"Answer\",\"position\":2,\"encodingFormat\":\"text/markdown\",\"text\":\"\u003cdiv\u003e2976 \u003cbr\u003e\u003c/div\u003e\",\"comment\":{\"@type\":\"Comment\",\"text\":\"For air-filled solenoids, permeability \\\\( \\\\mu_r = 1 \\\\). Always check the unit consistency when using formulas.\"},\"answerExplanation\":{\"@type\":\"comment\",\"text\":\"To ascertain the quantity of turns in the solenoid, the inductance \\\\( L \\\\) formula is utilized:L=μN2AlWhere:L represents inductance (0.016 H)μ denotes permeability of free space (\\\\(4π \\\\times 10^{-7} \\\\, \\\\text{Tm/A}\\\\))N is the number of turnsA is the cross-sectional areal is the solenoid's length (0.81 m)The solenoid's cross-sectional area \\\\( A \\\\) is calculated as:A=πrr2Given a radius \\\\( r = 0.02 \\\\, \\\\text{m} \\\\), the area is computed:A=π(\u0026lt;/mo\u003e0.02)2Substituting values to find \\\\( A \\\\):=3.1416\times(\u0026lt;/mo\u003e0.02)2=1.25664\times10-3 m2Inserting this into the inductance formula yields:0.016=(\u0026lt;/mo\u003e4π\times10-7)N2(\u0026lt;/mo\u003e1.25664\times10-3)0.81Rearranging to solve for \\\\( N^2 \\\\):NN2=0.0160.81(\u0026lt;/mo\u003e4π\times10-7)\div(\u0026lt;/mo\u003e1.25664\times10-3)Finally, solving for \\\\( N \\\\):N=0.0160.81(\u0026lt;/mo\u003e4π\times10-7)\div(\u0026lt;/mo\u003e1.25664\times10-3)The computed number of turns is approximately \\\\( N \\\\approx 2976 \\\\).\"}}}]}"},"notifications":{},"isMathJx":true},"isMobile":false}},"page":"/exams/questions/[slug]","query":{"slug":"[slug]"},"buildId":"Pxxpps6cIJqBA_Wm1PRv8","assetPrefix":"https://static.zollege.in/zollege-ques-prod-next/0.0.4","isFallback":false,"dynamicIds":[42867,49631,19808,70829,38073,68003,47969,73033,4187,77871,12455,47617,59423,78157,14558,45622,60727,92402,46066,60551,95421,14653,50751,84588],"gip":true,"appGip":true,"scriptLoader":[]}

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:

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The Correct Option is C

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Top Questions on Electromagnetic induction

Questions Asked in CBSE Class XII exam