1.

An inverted L shaped conductor PRQ is made by joining two perpendicular conducting rods, each of length 1.5 L, at end R. This structure is moving in x-y plane containing variable magnetic field vec(B) = -3xhate(k) with a velocity vhate(i) + vhat(j). If potential of P is V_(p) and that of Q is V_(Q), then value of V_(P) - V(Q) at the instant when P is at origin as shown in Fig. Will be

Answer»

`(9vL^(2))/(8)`
`(27vL^(2))/(8)`
`-(9vL^(2))/(8)`
`-(27vL^(2))/(8)`

Solution :`V_(R)-V_(P)=int(vec(v) xx vec(B))*dvec(e)`
`=int (v hat(i)+vhat(j)) xx (-3 xhat(K))*dxhat(i)`
`=3V int x(-hat(j)+hat(i)).dxhat(i)`
`V_(Q)-V_(R)=int (vhat(i)+v hat(j)) xx (-3(1.5L)hat(k)).dy hat(j)`
`=-4.5 vL int(-hat(j)+hat(i)).dyhat(j)`
`=4.5 vl int_(0)^(1.5L_ dy=(27)/(4) vL^(2)`
from above
`V_(P)-V_(Q)=27/8 vL^(2)-27/4 vL^(2)=(-27)/(8) vL^(2)`.


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