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Question

A square loop of 2 m side is placed in xy-plane with its centre at the origin and sides along the coordinate axes. If the magnetic flux density in the region is given by,

B=(2ˆax+3ˆay+5ˆaz)e0.5tWb/m2


The emf induced in the loop at t = 10 sec will be _____ mV
  1. 67.379

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Solution

The correct option is A 67.379

At any time instant the magnetic flux enclosed by the loop is

ϕ=B.ds

as the loop in xy plane

ϕ=1111Bzdxdy

ϕ=11115ˆaz.e0.38ˆazdxdy=11115e0.5tdxdy=5e0.5t(2)(2)

=20e0.5tWb

Induced emf=dϕdt=20ddte0.5t

=20(0.5)e0.5t

At t = 10 sec,

Induced emf=10e0.5×10=0.067V=67.379 mV


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