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A plane loop is shaped as two squares (F...

A plane loop is shaped as two squares (Fig) and placed in a uniform magnetic field at right angle to the loop's plane. The magnetic induction varies with time as `B =B_(0) sin (omega)t, where B_(0) = 10 mT and (omega) = 100 rads^(-1)`. The wires do not touch at point A. If resistance per unit length of the loop is `50 m(Omega)// m`, then amplitude of current induced in the loop is

A

`1.5A`

B

`1.0A`

C

`0.5A`

D

`2.0A`

Text Solution

Verified by Experts

The correct Answer is:
C
Induced emf's in the two loops will oppose each other. So net induced emf:
`e=(d)/(dt)[(b^(2)-a^(2))B]=(b^(2)-a^(2))(dB)/(dt)`
`=(0.20^(2)-0.10^(2)) (omega B_(0)cos (omega)t`
`=(0.04-0.01)xx100xx10xx10^(-3) cos (omega)t`
`=30xx10^(-3) cos (omega)t`
Resistance : `R=50xx10^(-3)[4xx20+4xx10]=60xx10^(-3) (Omega)`
`I=e/R 0.5(omega)t`
so aamplitude of current `=0.5A`.
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