A `pi` shaped metal frame is located in a uniform magnetic field perpendicular to the plane of the conductor and varying with time at the rate `(dB//dt)=0.I0T//sec` . A conducting connector starts moving with an acceleration `a=I0cm//sec^(2)` along the parallel bars of the frame. The lenght o0f the connector is equal to `l=20cm` . Find the emf induced in the loop `t=2sec` after the beginnig of the motion, if at the moment `t=0` the loop area and the magnetic induction are equal to zero. The inductance of the loop is to be neglected.

Explanation

The flux through the loop changes due to the variarion in `vec(B)` with time and also due to the movement of the connector.
So, `xi_(In) = |(d(vec(B).vec(S)))/(dt)| = |(d(BS))/(dt)|` as `vec(S)` and `vec(B)` are colliniear
But, `B`, after `t` sec of begining of motion = `Bt`, and `S` becomes `= l (1)/(2) w t^(2)`, as connector starts moving from rest with a constant accelertion `w`.
So, `xi_("ind") = (3)/(2) B l w t^(2)`