Question

Consider a long, straight wire of cross-sectional area A carrying a current i. Let there be n free electrons per unit volume. An observer places himself on a trolley moving in the direction opposite to the current with a speed $v=\frac{i}{nAe}$ and separation from the wire by a distance r. The magnetic field seen by the observer is very nearly
(a) $\frac{{\mathrm{\mu }}_{0}i}{2\mathrm{\pi }r}$
(b) zero
(c) $\frac{{\mathrm{\mu }}_{0}i}{\mathrm{\pi }r}$
(d) $\frac{2{\mathrm{\mu }}_{0}i}{\mathrm{\pi }r}$

Answer 1

(a) $\frac{{\mathrm{\mu }}_{o}i}{2\mathrm{\pi }r}$
Magnetic field will be independent of the motion of the observer because the velocity with which the observer is moving is comparable to drift velocity of electron which is very small as compared to the speed of flow of current from one end of wire to other end. So it can be neglected and hence, magnetic field due to the wire w.r.t the observer will be
B = $\frac{{\mathrm{\mu }}_{o}i}{2\mathrm{\pi }r}$


μ0i2πr