Question

Magnetic field in the region is given by B = 2t T as shown in figure. Conducting rod of length L = 1 m starts moving with constant speed of v = 2 m/s at t = 0 and at $x_0=8m$. Time when current in resistor changes its direction is

Answer 1

$\varphi =B.A=B_{0}tLx$

$ϵ=\frac{d\varphi }{dt}=B_{0}L\frac{d}{dt}\left(tx\right)$

$ϵ=B_{0}L[x-tv]$

$ϵ=B_{0}L[x_0-2vt]$

$ϵ=0\Rightarrow t=\frac{x_0}{2v}=\frac{8}{2\times 2}=2sec$