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

In time `t` , distance travelly by conductor `b=(1)/(2)at^(2)`
Flux passing through loop
`phi=BA=Blb=(Blat^(2))/(2)`
Here `B` and `t` both are vartiable
`e=(dphi)/(dt)=(la)/(2)[(dB)/(dt)t^(2)+B.2t]`
`=(0.2xx0.1)/(2)[0.1xx(2)^(2)+2Bxx2]`
`=10^(-2)[0.4+4B]`
`(dB)/(dt)=0.1`
`dB=0.1dt`
`int_(0)^(B)dB=0.1int_(0)^(1)dt`
`B=0.1t=0.1xx2=0.2`
`e=10^(-2)[0.4+4xx0.2]=1.2xx10^(-2)V`