Question

A straight long wire is carrying current I. The ratio of magnetic field due to this wire at perpendicular distance 2 cm and 5 cm respectively from the wire is

• A. \(2:5\)
• B. \(3:5\)
• C. \(7:3\)
• D. \(5:2\)

Hint:

B = mu0 I / (2 pi r), so B is inversely proportional to distance.

Answer 1

The Correct Option is D

Step 1: Put numbers in:
$B_1 = \dfrac{\mu_0I}{2\pi(0.02)}$ and $B_2 = \dfrac{\mu_0I}{2\pi(0.05)}$.

Step 2: Divide:
$\dfrac{B_1}{B_2} = \dfrac{0.05}{0.02} = 2.5 = \dfrac52$.

Step 3: Sense check:
The nearer point is 2 cm from the wire and has the stronger field, so the first number in the ratio must be larger.

Step 4: Why the nearer point has a stronger field:
The field of a long wire falls as 1/r, so moving closer by a factor 2.5 raises the field by the same factor. The point at 2 cm is 2.5 times nearer than the point at 5 cm, so its field is 2.5 times larger, which is the ratio 5:2.

Final Answer:
Option (D). \[ \boxed{5:2 \text{ (D)}} \]