The magnetic field inn a region is given by `vec B = veck (B_0)/(L) y` where L is a fixed length. A conducting rod of length L lies along the Y - axis between the origin and the point (0,L, 0). If the rod moves with a velocity `v= v_0` , find the emf induced between the ends of the rod.

Explanation

Here magnetic field is variable at every point of rod. Taking an element of length `dy` at distance `y` .
`de=Bvdy`
`e=(B_(0)v)/(L)int_(0)^(L)ydy`
`=e=(B_(0)V)/(L).|(y^(2))/(2)|_(0)^(L)=(1)/(2)B_(0)vL`
This rod can be replaced by a battery of emf `e=B_(0)vL//2` and negative terminal is that end towards which electrons are movig due to magnrtic force.