Question

A 23-turn circular coil of radius 3.40 cm and resistance 1.00 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.010 0t + 0.040 0t2, where B is in teslas and t is in seconds.

Calculate the induced emf in the coil at t = 5.40 s.

Answer 1

Emf will be
`36.8* 10^(-3)volt`

Step-by-step explanation:

We have given number of turns N = 23

Radius of the coil r = 3.40 cm = 0.034 m

So area of the coil
`A=\pi r^2=3.14* 0.034^2=0.00362m^2`

Magnetic field is given as
`B=0.01t+0.04t^2`

We have to find the emf at t = 5.4 sec

We know that emf is given by

`e=A(dB)/(dt)=0.00362* (d(0.01t+0.04t^2))/(dt)`

`e=NA(dB)/(dt)=0.00362*(0.01+0.08t)`

So emf at t = 5.4 sec

`e=23*0.00362*(0.01+0.08* 5.4)=36.8* 10^(-3)volt`