Physics EM induction

Question

A pair of parallel conducting rails that are L = 22 cm apart lies at right angles to a uniform magnetic field of 0.5 T directed into the page. A R = 14  resistor is connected across the rails. A conducting bar is moved to the right at 2 m/s across the rails.

What is the current in the resistor? 

What is the magnetic force on the bar due to the induced current? 

Answer 1

This problem is an application of Faraday's Law of Induction. Faraday's Law states that the induced electric voltage is due to the CHANGE in the magnetic flux in the loop.

The total magnetic flux will be the product of the B field and the rectangular area enclosed by the two rails, the resistor connecting them at one end, and the moving bar connecting them at the other end. This is a common problem in the course and gives a result that the emf/voltage will be B x height x speed of the loop as it enters the magnetic field. Don't forget to convert units to mks. Remember what you just learned about resistors and circuits. Apply Ohm's Law to obtain the current flowing around the loop.

The second part of the question is another topic you learned a few chapters ago: the force on a length of wire carrying a current I in a uniform magnetic field is equal to the current times the cross product of the the length of the wire with the magnetic field. This problem assumes the two are perpendicular and only asks about the magnitude so you can use the relationship that magnitude of the vector A cross the vector B = Product of the magnitudes of A and B times the sine of the angle between them.