Question

A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as shown in Fig. Terminals aand b of winding Amay be connected to a battery through a reversing switch. State whether the induced current in the resistor R is from left to right or from right to left in the following circumstances:

(a) the current in winding A is from ato band is increasing;

(b) the current in winding Ais from bto aand is decreasing;

(c) the current in winding Ais from bto aand is increasing.

Short answer

1. From right to left.
2. From right to left.
3. From left to right

Step-by-step solution

Concept.

Definitions

Lenz's law: Lenz's law states that an induced current or emf always tends to oppose or cancel out the change that caused it.

Right-hand rule for a magnetic field produced by a current in a loop: When the fingers of your right hand curl in the direction of the current, your right thumb points in the direction of the magnetic field lines.

Finding part (a) of the problem.

When the current in winding A is from a to b and is increasing;

Using the right-hand rule on the coil, we curl the fingers of the right hand, and we find that the right thumb is pointing to the left.

Since the current is increasing, the magnetic field is also increasing at the coil of winding B.

Applying Lenz's law, this change in the magnetic field at winding B induces a current in winding B to oppose this change

So, the magnetic field produced by the induced current is to decrease the magnetic field to the left

Thus, the magnetic field produced by the oil of winding B is to the right

Using the right-hand rule, point your right thumb in the direction of the magnetic field to the right, so your right fingers now curl in the direction of the induced current

Following the direction of the induced current, we find it flows through the resistor R from right to left

Finding part (b) of the problem.

When the current in winding A is from b to a and is decreasing:

Using the right-hand rule on the coil, we curl the fingers of the right hand, and we find that the right thumb is pointing to the right

Since the current is decreasing, the magnetic field is also decreasing at the coil of winding B.

Applying Lenz's law, this change in the magnetic field at winding B induces a current in winding B to oppose this change.

So, the magnetic field produced by the induced current is to increase the magnetic field to the right

Thus, the magnetic field produced by the coil of winding B is to the right

Using the right-hand rule, point your right thumb in the direction of the magnetic field to the right, so your right fingers now curl in the direction of the induced current.

Following the direction of the induced current, we find it flows through the resistor R from right to left.

Finding part (c) of the problem.

When the current in winding A is from b to a and is increasing

Using the right-hand rule on the coil, we curl the fingers of the right hand, and we find that the right thumb is pointing to the right

Since the current is increasing, the magnetic field is also increasing at the coil of winding B.

Applying Lenz's law, this change in the magnetic field at winding B induces a current in winding B to oppose this change

So, the magnetic field produced by the induced current is to decrease the magnetic field to the right

Thus, the magnetic field produced by the coil of winding B is to the left.

Using the right-hand rule, point your right thumb in the direction of the magnetic field to the left, so your right fingers now curl in the direction of the induced current

Following the direction of the induced current, we find it flows through the resistor R from left to right.