Question

the magnetic field due to an arc of current varies with the radius r as 1. $\frac{1}{r}$ 2. $\frac{1}{r^{2}}$ 3. r 4. r²

Explanation:

Step1: Recall Bi - ot Savart law

The magnetic field due to a current - carrying arc of length $l$ at the center of the circle of radius $R$ is given by $B=\frac{\mu_0 I l}{4\pi R}$, where $\mu_0$ is the permeability of free space, $I$ is the current and $l$ is the length of the arc. For a fixed current $I$ and arc - length $l$, $B\propto\frac{1}{R}$.

Answer:

$\frac{1}{R}$