A magnetic field given by B(t) `=0.2t-0.05t^(2)` tesla is directed perpendicular to the plane of a circular coil containing 25 turns of radius 1.8 cm and whose total resistance is `1.5Omega`. The power dissipation at 3 s is approximately

Options

A. `1.37muW`
B. `7muW`
C. zero
D. `4muW`

Answer

D

Explanation

Magnetic flux
`phi=NBA=(25)(pi)(1.8xx10^(-2))^(2)[0.2t-0.05t^(2)]`
`=0.025(0.2t-0.05t^(2))`
Induced emf, `e=|(dphi)/(dt)|=|0.025(0.2-2xx0.05t)|`
At t = 3 s, e = 0.0025 V
`i=(e)/(R)=0.0016A`
`therefore` Power dissipation, `P = ei=4xx10^(-6)W=4mu W`