Question

The magnitude of the magnetic field at a certain distance from a long, straight conductor is represented by B. What is the magnitude of the magnetic field at twice the distance from the conductor?A. At twice the distance, the magnitude of the field is 4B.B. At twice the distance, the magnitude of the field is 2B.C. At twice the distance, the magnitude of the field is B/2.D. At twice the distance, the magnitude of the field is B/4.E. At twice the distance, the magnitude of the field remains equal to B.

Answer 1

Answer:

C. At twice the distance, the magnitude of the field is B/2

Explanation:

The strength of the magnetic field produced by a current-carrying wire is:

$B=\frac{\mu_0 I}{2\pi r}$

where

$\mu_0$ is the vacuum permeability

I is the current

r is the distance from the wire

If we double the distance,

r' = 2r

so the new magnetic field strength will be

$B'=\frac{\mu_0 I}{2\pi (2r)}= \frac{1}{2}(\frac{\mu_0 I}{2\pi r})=\frac{B}{2}$

So, the correct option is

C. At twice the distance, the magnitude of the field is B/2