Question

A conducting bar is sliding to the right on two rails which are connect by a 15 LaTeX: \Omega resistor. The distance between the rails is L = 0.50 m. There is a uniform magnetic field with a magnitude of 0.80 T as shown in the figure. (a) Find the speed at which the bar must be moved to produce a current of 0.2 A in the resistor. Ignore the resistance in the rails and conducting bar. sa007-1.jpg (b) What is the direction of the induced magnetic field and induced current in the system? Explain reasoning.

Answer 1

The induced emf is given by the change in magnetic flux through the loop is
= - d / dt
= d (B . A) / ft
Where B is the magnetic strength and A is the crossectional area of the loop.
A = L . x
Where x is the horizontal distance the bar covers at time t.
= B d (L x)/dt
= B x L x v
The induced current
i = / R = B x L x v / R
We need to find the speed v to have an induced current of 0.2 A
v = I R / B L
v = 0.2 A x 15 /   0.80 T x 0.5 m
v = 7.5 m/s
b) The induced magnetic field and the induced current will be directed in such a way that it opposes the change in magnetic flux.
If the original mangetic field is directed into the page, then as the wire moves to the right, more area comes into the system and thus magnetic flux is increasing, To oppose this effect, another magnetic field is induced in such a way that the net magnetic field is reduced. The induced magnetic field then should direct out of the page. This magnetic field is produced by the current going in counter-clockwise direction.