Question

Magnetic field intensity at the centre of coil of 50 turns, radius 0.5 m and carrying a current of 2 A, is

• A. $3 \times {10}^ {-5} \,T $
• B. $1.25 \times {10}^ {-4} \,T $
• C. $0.5 \times {10}^ {-5} \,T $
• D. $4 \times {10}^ {6 }\,T $

Answer 1

The Correct Option is B

To calculate the magnetic field intensity at the center of a coil, we use the formula for the magnetic field at the center of a circular coil carrying current:

B = \frac{{\mu_0 \cdot N \cdot I}}{{2 \cdot R}}

Where:

• \mu_0 is the permeability of free space, \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A}
• N is the number of turns in the coil
• I is the current flowing through the coil
• R is the radius of the coil

Given values:

• N = 50
• I = 2 \, \text{A}
• R = 0.5 \, \text{m}

Substitute these values into the formula:

B = \frac{{4\pi \times 10^{-7} \cdot 50 \cdot 2}}{{2 \cdot 0.5}}

Calculating further:

B = \frac{{4\pi \times 10^{-7} \cdot 100}}{{1}}

B = 4\pi \times 10^{-5} \, \text{T}

Using \pi \approx 3.14:

B \approx 4 \times 3.14 \times 10^{-5}

B \approx 12.56 \times 10^{-5}

B \approx 1.256 \times 10^{-4} \, \text{T}

Approximating as given in the options, B \approx 1.25 \times 10^{-4} \, \text{T}, which matches the correct answer.

Therefore, the correct answer is 1.25 \times 10^{-4} \, \text{T}.