A square loop of side 12 cm and resistance `0.06Omega` is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T is set up across the plane in north-east direction. The magnetic field is decreased to zero in 0.6 s at steady rate. The magnitude of current during this time interval is

Options

A. `1.42xx10^(-3)A`
B. `2.67xx10^(-3)A`
C. `3.41xx10^(-3)A`
D. `4.21xx10^(-3)A`

Answer

B

Explanation

Here, Area `A=l^(2)=(12cm)^(2)=1.4xx10^(-2)m^(2)`
`R=0.60Omega,B_(1)=0.10T.theta=45^(@)`
`B_(2)=0,dt=0.6s`
Initial flux, `phi_(1)=B_(1)Acostheta`
`=0.10xx1.4xx10^(-2)xxcos45^(@)`
`=9.8xx10^(-4)Wb`
Final flux, `phi_(2)=0`
Induced emf, `epsi=(|dphi|)/(dt)=(|phi_(2)-phi_(1)|)/(dt)`
`=(|9.8xx10^(-4)|)/(0.6s)=1.6xx10^(-3)V`
Current,
`I=(epsi)/(R)=(1.6xx10^(-3))/(0.6)=2.67xx10^(-3)V`