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A thin wire of length 2m is perpendicula...

A thin wire of length `2m` is perpendicular to the `xy` plane. It is moved with velocity
`vec(V)=(2hat(i)+3hat(j)+hat(k))m//s` through a region of magnetic induction `vec(B)=(hat(i)+2hat(j))Wb//m^(2)`. Then potential difference induced between the ends of the wire:

A

`2`Volts

B

`4` volts

C

`0` volt

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`e=-(vec(V)xxvec(B)).vec(l)`
`vec(V)xxvec(B)=(2hat(i)+3hat(j)+hat(k))xx(hat(i)+2hat(j))=-2hat(i)-hat(j)+hat(k)`
`e=-(vec(V)xxvec(B)).vec(l)=(2hat(i)-hat(j)+hat(k)).2hat(k)=2` volt
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