Question

When a magnet is thrust into a coil as in Figure 23.4(a), what is the direction of the force exerted by the coil on the magnet? Draw a diagram showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the force depend on the resistance of the galvanometer?

Short answer

The force is in the opposite direction of the motion of the magnet.

The diagram is shown below.

The resistance of the galvanometer affects the current in the magnetic coil. As a result, if the resistance is low, the current and force will be higher. More resistance reduces current and thus force.

Step-by-step solution

Definition of magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving charges, currents, and magnetic materials. A moving charge in a magnetic field is subjected to a force that is perpendicular to both its velocity and the magnetic field.

Explanation

The force produced always resists the motion of the magnet, the force is always directed downward.

When a magnet is inserted into a coil, a current is induced in the coil, and the magnetic strength increases. This current generates a field in the opposite direction to counteract the increase in magnetic strength. This field opposes the magnet's motion. As a result, it exerts a force in the opposite direction of the motion. Consider the following diagram, which depicts the direction of the current induced in the coil as well as the magnetic field produced:

Applying the Ohm's law

Because the magnetic field's direction is upward. As a result, the force produced is downward. The right-hand rule can be used to determine the direction of the current. This rule states that the thump points in the direction of motion, the first finger points in the direction of the magnetic field, and the second figure points in the direction of the current. In the diagram, apply this rule. The current flows in a clockwise direction.

Consider Ohm's law:

\(V = IR\)

V denotes voltage, I denotes current, and R denotes resistance.

This law states that:

\(I \propto \frac{1}{R}\)

Thecurrent is inversely proportional to resistance, and force is directly proportional to the current flowing through the coil.

As a result, the magnitude of the force is inversely proportional to the galvanometer's resistance.