Find `oint vec(B).vec(dl)` over following loops (direction in which integration has to be performed is indicated by arrows)

If oint_(S) vec(E ).vec(dS) = 0 over a surface then,

If underset s oint vecE.vec(ds)=0 over a surface, then

You are given two vectors vec A and vec B . Which one of the following operation cannot be performed ?

Find oint B. dl for the paths shown in (a) and (b)

Find the values of ointvecB.vec(dl) for the loops L_1, L_2 and L_3 in Fig. (The sense of vec(dl) is mentioned in the figure)

Find the values of ointvecB.vec(dl) for the loops L_1, L_2 and L_3 in Fig. (The sense of vec(dl) is mentioned in the figure)

Find the values of ointvecB.vec(dl) for the loops L_1, L_2 and L_3 in Fig. (The sense of vec(dl) is mentioned in the figure)

A closed current-carrying loop having a current I is having area A. Magnetic moment of this loop is defined as vec(mu) = vec(IA) where direction of area vector is towards the observer if current is flowing in anticlockwise direction with respect to the observer. If this loop is placed in a uniform magnetic field vec(B) , then torque acting on the loop is given by vec(tau) = vec(mu) xx vec(B) . Now answer the following questions: Let ring in the above question is having a radius R and a charge Q is uniformly distributed over it. Ring is rotated with a constant angular velocity (omega) as mentioned above. Torque acting on the ring due to magnetic force is