Question

How is Faraday’s /Lenz law consistent with the magnetic force on a moving charge? An example may help. That is, find an example where Faraday’s/Lenz laws predict the same direction of current as the magnetic force equation.

In question 200 we were asked to find three fundamental ways in which we predicted we could induce an Emf using Faraday’s Law. We will now explore examples of them. A 3.5 T field faces the same way as a 20.0 Ù loop of radius 5.00 cm. a) The field is turned off in 4.00 seconds. Find the average voltage and current induced. b) The loop is flipped over in 4.00 seconds. Find the average voltage and current induced. c) The loop is squished into a flat rectangle 2.00 cm wide in 4.00 seconds. Find the length of the loop and the average voltage and current induced.

Answer 1

a). emf = - d/dt (flux) = - d/dt (BA) = - A d/dt B
To calculate the average, we can replace dB/dt with (delta B)/(delta t).
<emf> = - A (delta B)/(delta t)
= - (0.0079 m^2)(-3.5 T)/(4 s) = 0.0069 V

Induced current = 0.0069/20 = 0.34 mA (20ohm is the resistance )

b). emf= (2/pi) x 0.05 x 0.05 x 3.5 x d(theta)/dt x [cos-180 + cos0]

d(theta)/dt= pi/dt= 3.14/4

emf = 8.75 mV

I = 8.75/20 = 0.44 mA

c). Perimeter is same

So, 2(l+b) = 2*pi*5

l = 13.7cm

emf = 3.5 x 0.137 x 0.02/4 = 2.4 mV

Current = 2.4/20 = 0.12 mA