Question

A circular coil of radius 5.0 cm and resistance 0.20 Ω is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B = 0.50e-20t T.What is the magnitude of the current induced in the coil at the time t = 2.0 s?

Answer 1

Answer:

The induced current in the coil at the time 2 s is 0.00263 A

Explanation:

The equation for induced emf is equal to:

$\epsilon =-\frac{d}{dt} (BAcos\theta )$

Where

B = magnetic field

A = area

θ = angle

$\epsilon =-Acos0\frac{d}{dt} B\\\epsilon =-(\pi r^{2} )\frac{d}{dt} (0.5e^{-0.2t} )\\\epsilon =0.1 (\pi r^{2} )e^{-0.2t}$

For t = 2 s

$\epsilon =0.1*\pi *0.05^{2} *e^{-0.2*2} =5.26x10^{-4} V$

The induced current is:

$I=\frac{\epsilo }{R} =\frac{5.26x10^{-4} }{0.2} =0.00263A$