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=inAe and separation from the wire by a distance r. The magnetic field seen by the observer is very nearly
(a) μ0i2πr
(b) zero
(c) μ0iπr
(d) 2μ0iπr

Answer 1

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=inAe and separation from the wire by a distance r. The magnetic field seen by the observer is very nearly (a) B =  μoi/2πr  

Explanation:

• The magnetic field will be independent of the observer's motion because the observer's velocity of movement is comparable to the electron's drift velocity which is very small compared to the current flow rate from one end of the string to the other end.
• So it can be avoided and therefore, the magnetic field due to the wire with respect to observer is   $B = \frac{\mu_0i}{2\pi r}$  

Therefore the correct answer is Option (a)

Answer 2

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Option A is correct