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

Answer 2

At twice the distance, the magnitude of the magnetic field is B/2 due to increase in the distance between them.

Strength of magnetic field is inversely proportional to the distance of a conductor. If the distance of an object is decrease, its magnetic field increase while on the other hand, if the distance is decrease the intensity of magnetic field on that object or charge increases.

The strength of the magnetic field at its peak near to the source but moving away from it gradually decreases the strength of the magnetic field so we can conclude that double the distance, the magnitude of magnetic field become half.

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