Two straight conducting rails form a right angle where their ends are joined. A conducting bar in contact with the rails starts at the vertex at time t = 0 and moves with constant velocity v along them as shown in Fig. A magnetic field `vec(B)` is directed into the page. the induced emf in the circuit at any time t is proportional to

Options

A. `t^(@)`
B. `t`
C. voltage across L is equal to zero.
D. `v^(2)`

Answer

B, D

Explanation

Let `/_CAE = alpha =` constant

At time `t, DE=vt`
`AD=DE tan alpha`
and `DC=DE tan alpha` ltbr. `AC=DE(tan alpha+ cot alpha)`
`=vt(tan alpha+cot alpha)=1 (sqy)`
Induced emf `e=Bvl`
`e=Bv^(2)t (tan alpha + cot alpha)`
`e prop v^(2) and e prop t`.