Induction and Energy Transfers Revision Notes

In these revision notes for Induction and Energy Transfers, we cover the following key points:

• The relationship between magnetic and electric field in terms of induction
• What happens when we do some work to move a coil inside a magnetic field
• How to change the magnetic flux inside a coil placed inside a magnetic field
• What is the rate of work done by an external source on a coil placed inside a magnetic field
• How the emf induced in a moving coil is related to the external magnetic field?
• The same for the current induced in a moving coil inside a magnetic field
• What are eddy currents and how they are produced?

Induction and Energy Transfers Revision Notes

Induction results in a transfer of energy between the parts of a system. If the energy lost due to radiation is neglected, we say that the faster the magnet is moved, greater the work done by the external force in a certain time and therefore, greater the rate of energy transfer in the loop. This means the power of this energy transfer is greater when the magnet moves faster.

The moving direction of magnet is not important; as long as the magnet is moving, it transfers energy to the coil.

The magnetic flux produced when we move a coil inside a uniform magnetic field can change in two ways:

1. By pulling the coil at non-uniform velocity, for example pulling it by applying an increasing or decreasing force. In this case, the flux changes due to the change in the number of magnetic field lines, despite the area is the same.
2. By moving the coil in or out of magnetic field. In this case, the area in which the magnetic field lines punch the coil is changing. Thus, when we insert the coil inside the magnetic field the area increases, so the flux increases (remember that magnetic flux in uniform field is Φ = B ∙ A). On the other hand, when we move the coil out of the field the flux decreases as the area punched by magnetic field lines decreases.

The magnitude of the induced emf in the coil is

where w is the width of the rectangular coil and v is its moving velocity.

Giving that the magnetic force produced in a current carrying wire is

we obtain for the magnetic force induced in the coil

The last equation means that if the magnetic force F_m is constant, the moving speed v of the coil is constant as well. This is because the other parameters such as the magnetic field B, the width of loop w and the resistance R are all constants.

The rate of work (i.e. the mechanical power) done by the external force F when moving the coil inside a uniform magnetic field is

As for the rate of thermal energy produced in the coils, we have:

The above two equations give the same value. This means the work done for pulling the loop through a magnetic field is transferred entirely to the loop in the form of thermal energy.

The circular currents produced when we replaced the rectangular frame with a solid rectangular plate are known as eddy currents (eddy = whirlpool).