Question

A plane loop, shaped as two squares of sides `a = 1m` and `b = 0.4m` is introduced into a uniform magnetic field `_|_` to the plane of loop . The magnetic field varies as `B = 10(-3)sin(100t) T`. The qamplitude of the current induced in the loop if its resistance per unit length is `r = 5 mOmega m^(-1)` is

A. (a) `2 A`
B. (b) `3 A`
C. ( c) `4 A`
D. (d) `5 A`

Answer 1

Correct Answer - B
( b) `phi ( "flux linked") = a^(2)B cos0^(@) - b^(2)Bcos 180^(@)`
`= (a^(2) - b^(2))B`
`E = -(dphi)/(dt) = -(a^(2) - b^(2))(dB)/(dt)`
`= (a^(2) - b^(2)) B_(0) omega cos omegat`
where `B = B_(0)`, ` sinomega t`, `B_(0) = 10^(-3) T`, `omega = 100`
`:.` `I_(max) = (a^(2) - b^(2))(B_(0)omega)/(R)`
and :. `I_(max) = ((a - b)B_(0)omega)/(4r) = ((1 - 0.4) xx 10^(-3) xx 100)/(4 xx 5 xx 10^(-3)) = 3A`