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Q.

A semicircular conducting metallic loop of radius R is moving in x-y plane in a region of uniform magnetic field given by B=B0[i^+2j^+3k^] with velocity V=V0i^ as shown in diagram. Then

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a

point B and point C will be at same potential

b

induced emf across its ends will be33V0B0R

c

we can get two points on loop which will be at same potential

d

potential of end C is less than potential of end A

answer is A, B.

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Detailed Solution

V¯=V0i^;

B¯=B0[i^+2j^+3k^]

l¯=2r12i^+2r32j^

=ri^+r3j^

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FromE=(V¯×B¯).l¯

E=33V0B0R

Look at component3k^  in the magnetic field C will be at lower potential and A will be at higher potential

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