First slide

Induced Electric Field and Magnetic field

Question

A coil having n turns and resistance R $Ω$ is connected with a galvanometer of resistance 4 R $Ω$ . This combination is moved in time t seconds from a magnetic field B₁ weber to B₂ weber. The induced current in the-circuit is

Easy

A

$\frac{B_{2} - B_{1}}{5 Rnt}$
B

$- \frac{n (B_{2} - B_{1})}{5 Rt}$
C

$- \frac{(B_{2} - B_{1})}{Rnt}$
D

$- \frac{n (B_{2} - B_{1})}{Rt}$

Solution

The rate of change of flux or e.m.f. induced in the coil is given by
$e = - n \frac{dΦ}{dt}$
Induced current $i = \frac{e}{R^{'}} = - \frac{n}{R^{'}} \frac{dΦ}{dt} . . . . (1)$
$Here, R^{'} = R + 4 R = 5 R, dΦ = B_{2} - B_{1} and dt = t ∴ i = - \frac{n}{5 R} \frac{(B_{2} - B_{1})}{t}$

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