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Question

A uniform magnetic field exists in a region given by B=3^i+4^j+5^k. A rod of length 5m along y-axis moves with a constant speed of 1m s1 along x axis. Then the induced emf in the rod will be

A
0
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B
25V
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C
20V
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D
15V
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E
none
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Solution

The correct option is B 25V

Given,B=3+4+5k

V=1m/s(As the rod moves in XDirection)

Length of rod=5m

Since,e=dϕ/dt and ϕ=B.A
So,e=d(B.A)/dt
e=d(B.A)/dt(Negative sign is neglected as it only represents the direction)
e=B.d(A)/dt(Magnetic Field is constant)
=B.d(l×b)/dt(Where l=Length and b=Breadth)
=lB.d(b)/dt(1)
As db/dt is nothing but the velocity with which the rod is moving.

So,db/dt=V

Putting the above value of db/dt in equation (1)
We have, e=lB.V

But, in the above equation it is assumed that the direction of B, L and V are mutually perpendicular.

So, Only that component of B that is in mutual perpendicular direction of L and V will be taken into account.

So,e=lB.V=5×5×1

e=25V

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