Self Assessment Quiz

1. A conducting bar of resistance R slides frictionlessly with a constant speed upward over  a pair of resistanceless rails inclined at an angle 2q under the action of some external force. A uniform magnetic field of strength B subsists in the region perpendicular to the plane of the rails as shown. Find the current induced in the circuit both by direct use of Faraday’s law and by explicit use of Lorentz force for calculation of motional emf.

2. A rectangular conducting loop of width w , length L  and resistance R falls under gravity keeping its plane always vertical . An inhomogeneous magnetic field  points into the page (xy) plane).  Find the terminal velocity of the loop.

3. A circular loop  of radius R rotates with an angular speed  in a uniform magnetic field directed along the x axis. The loop rotates about an axis  parallel to the z axis.  Calculate the emf induced in the loop.

4. A long coaxial cable consists of a thin wire surrounded by a concentric shell of radius R. Current goes up through the wire and returns through the shell. If the current varies with time at a constant rate , calculate the emf developed and the induced electric field  in the rectangular loop of side  shown in the figure.