Chapter 25, Problem 71A

(a)

To determine

To Explain: The quantity that can be induced in the pipe.

Explanation of Solution

Introduction:

Eddy currents are the loops of current which are induced within the conductor that is caused by change in the magnetic field. This can be understood by the Faraday’s Law of Induction. The change in the magnetic field across a conductor will induce an emf.Eddy currents can flow in the closed loop which are in the planes at right angle to the magnetic field.

As per Lenz Law, an eddy current can generate a magnetic field which will oppose the change in the magnetic field that generated it, and then eddy currents react back to the source of the magnetic field.

Conclusion:

Hence,the changing magnetic field in the pipe induces eddy currents.

(b)

To determine

To Explain:

The way induced quantity in the pipe affects the falling magnet.

Explanation of Solution

Introduction:

Gravitational energy is a kind of potential energy which is associated with the gravitational field. Whenever one drops any object, the gravitational potential energy decreases.

Thermal energy is produced when there is rise in the temperature that causes the movement of the atoms and molecules to move fast and collide with each other.

Kinetic Energy of an object is defined as the energy that is caused due to the motion. It is the work which is needed to move the body with a given mass from its rest position to the stated velocity.

The magnetic field generated by the eddy currents resist the magnetic field of the magnet and thus, the fall of the magnet slows down.

When one drops a magnet, the gravitational potential energy is decreased, but there is addition of magnetic potential energy and kinetic energy. The eddy current causes the pipe to get warm. As the magnet falls down gravitational energy is decreases but the kinetic energy does not decrease. There is increase in the thermal energy of the pipe and it gets hot than the surrounding air and the heat is transmitted to the air.

(c)

To determine

To Explain:

Whether the fall of the magnet slows down if plastic pipe is used.

Explanation of Solution

Introduction:

Eddy currents are the result of changing magnetic flux. This can also be considered as the response of any conductor to a changing magnetic field. This current flows in closed loops and for the phenomenon to take place, good conductor of electricity is required.

Being a poor conductor, plastic pipe will not have eddy currents and would not able to slow down the motion of the magnet.

Conclusion:

Hence, a bad conductor of electricity pipe will not have eddy current and hence the magnet will not slow down.