Question

The magnetic flux can be estimated to be ΦB(t) = NB(t)A.

The coil is connected to two light bulbs in a series with a voltage of 6.6v

N=200 turns

A= 0.0314

The magnetic field is uniform over the area

B_o is the maximum value of the magnetic field

2π f=is more compactly written as the angular frequency

1) Use the expression   and the are (expressed in terms of the diameter) to write out an expression for the (time-dependent) magnetic flux:

Φ_b(t) =...

2) Then obey Faraday and find the induced voltage or EMF by taking the derivative with respect to time:

V_ind = − dΦ_B(t)/dt =...

Answer 1

1.Magnetic flux linked with the coil

$\phi = N*A*B(t)= 200*0.0314*B_0Sin(2\pi ft)$

$\phi = 6.28B_0Sin(2\pi ft)$

2. Induced emf by Faradays Law.

$V_{Ind}= -d\phi/dt = -[6.28B_0Cos(2\pi ft)]*(2\pi f)$

$V_{Ind}= -39.44fB_0Cos(2\pi ft)$