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A rectangular wire loop of sides 8cm and 2cm with a small cut is moving out of a region of the uniform magnetic field of magnitude 0.3T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1cms-1 in a direction normal to the (a) longer side and (b) shorter side of the loop? For how long does the induced voltage last in each case?


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Solution

Step 1: Given

Length of the loop, lr=8cm=0.08m

Width of the loop, br=2cm=0.02m

The magnetic field of the loop, B=0.3T

The velocity of the loop, v=1cms-1=0.01ms-1

Step 2: Formula used

Emf is in the loop, e=Blv
where, B is the strength of the magnetic field, l length of the object and v is the velocity.

Distance-time-speed relationship, time=distancespeed

Step 3: Solution

When loop is travelling in the normal direction to its length,

l=lr because it is moving along the normal to the length of the rectangle.

EMF developed in the loop,
e=Blrv=0.3×0.08×0.01=2.4×10-4V

Time taken to travel along the length,
t=lrv=0.080.01=8s

When loops is travelling along the normal to its breadth,

l=br because it is moving along the normal to the breadth of the rectangle.

EMF developing in the loop,
e=Bbrv=0.3×0.02×0.01=0.6×10-4V

Time taken to travel along the breadth,
t=brv=0.020.01=2s

Hence, the EMFs are 2.4×10-4Vand 0.6×10-4V and time 8s and 2s respectively.


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