Learn Unit 4-Electromagnetic Induction & Alternating Current with Free Lessons & Tips

To determine the direction of the induced current in the metallic loop when the electric current flows from B to A in the wire, we can apply Lenz's law.

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

In this case, when the current flows from B to A in the wire, it generates a magnetic field around the wire in the clockwise direction (using the right-hand grip rule). This magnetic field will intersect with the metallic loop.

Now, according to Faraday's law of electromagnetic induction, the change in magnetic flux through the loop induces an electromotive force (emf) and consequently an induced current.

To oppose the increase in the magnetic flux caused by the current flowing from B to A, the induced current in the metallic loop must generate its own magnetic field. By the right-hand rule, this induced magnetic field should be in the counterclockwise direction.

Therefore, the induced current in the metallic loop will flow in such a way that it generates a magnetic field in the counterclockwise direction, opposing the increase in magnetic flux caused by the current in the wire.

In summary, the induced current in the metallic loop will flow in the counterclockwise direction.

The time it takes for an object to fall freely from a certain height above the ground depends solely on its mass and the acceleration due to gravity, assuming air resistance is negligible.

Both the metallic and glass bobs have the same size, and when they are allowed to fall freely, they experience the same gravitational force. Since the gravitational force depends on the mass of the object, and both bobs have the same size, they will experience the same gravitational force regardless of their material composition.

Therefore, both the metallic and glass bobs will reach the ground at the same time when allowed to fall freely from the same height above the ground. This is because they experience the same gravitational acceleration and have the same mass (assuming their densities are equal, which is a reasonable assumption for objects of the same size).

Lenz's law states that the direction of the induced electromotive force (emf) in a circuit is such that it opposes the change in magnetic flux that produced it.

When a metallic rod held horizontally along the east-west direction is allowed to fall under gravity, it will experience a change in magnetic flux if there is a magnetic field present in the vicinity of the rod. However, for the scenario described, assuming there is no external magnetic field, there will be no change in magnetic flux experienced by the rod as it falls.

Since there is no change in magnetic flux, according to Faraday's law of electromagnetic induction, there will be no induced electromotive force (emf) generated in the rod. Faraday's law states that the emf induced in a circuit is directly proportional to the rate of change of magnetic flux through the circuit. If there is no change in magnetic flux, there will be no induced emf.

Therefore, in this scenario, as the metallic rod falls under gravity along the east-west direction without encountering any external magnetic field, there will be no emf induced at its ends.

Faraday's law of electromagnetic induction states that the electromotive force (emf) induced in a closed circuit is directly proportional to the rate of change of magnetic flux through the circuit. Mathematically, it can be expressed as:

emf=−dΦdtemf=−dtdΦ

Where:

• emfemf is the induced electromotive force (emf) in the circuit,
• ΦΦ is the magnetic flux through the circuit,
• tt is time.

In words, Faraday's law tells us that when there is a change in the magnetic field experienced by a circuit, an emf is induced in the circuit. This emf drives a current in the circuit, causing it to flow in such a way that it generates a magnetic field opposing the change in magnetic flux that produced it.

To predict the direction of the induced current in the loop PQRS when it is moved into a uniform magnetic field at right angles to the plane of the paper, we can apply Lenz's law.

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

In this case, as the loop PQRS is moved into the uniform magnetic field, the magnetic flux through the loop changes. According to Faraday's law of electromagnetic induction, a change in magnetic flux induces an electromotive force (emf) and consequently an induced current in the loop.

To oppose the increase in magnetic flux caused by moving the loop into the magnetic field, the induced current will flow in such a way that it creates a magnetic field opposing the external magnetic field.

Using the right-hand rule for the direction of induced current, if we imagine the magnetic field lines pointing out of the plane of the paper, the induced current will flow in such a way that it generates a magnetic field into the plane of the paper.

Therefore, the induced current in the loop PQRS will flow in the clockwise direction, as viewed from the top of the loop. This direction of the induced current creates a magnetic field into the plane of the paper, opposing the increase in magnetic flux caused by moving the loop into the magnetic field.

When the current II in the wire is steadily decreasing, the magnetic field around the wire decreases accordingly. According to Faraday's law of electromagnetic induction, this change in magnetic flux induces an electromotive force (emf) and consequently an induced current in nearby conductors.

Let's consider metal rings 1 and 2:

1. Metal Ring 1:

   • As the current in the wire decreases, the magnetic field around the wire also decreases.
   • Using Lenz's law, the induced current in metal ring 1 will flow in such a direction as to oppose the decrease in magnetic flux.
   • Therefore, the induced current in metal ring 1 will flow in a direction such that it creates a magnetic field in the same direction as the original magnetic field around the wire.
   • This means the induced current in metal ring 1 will flow clockwise when viewed from the top.

2. Metal Ring 2:

   • Similar to metal ring 1, the induced current in metal ring 2 will flow in such a direction as to oppose the decrease in magnetic flux.
   • Therefore, the induced current in metal ring 2 will flow in a direction such that it creates a magnetic field opposite to the original magnetic field around the wire.
   • This means the induced current in metal ring 2 will flow counterclockwise when viewed from the top.

In summary:

• The induced current in metal ring 1 will flow clockwise.
• The induced current in metal ring 2 will flow counterclockwise.

When a bar magnet is moved between two coils PQ and CD, the magnetic flux through each coil changes, inducing electromotive forces (emfs) and consequently inducing currents in the coils. To determine the directions of the induced currents in each coil, we can use Lenz's law.

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

Let's consider each coil separately:

1. Coil PQ:

   • As the bar magnet moves towards coil PQ, the magnetic flux through the coil increases.
   • According to Lenz's law, the induced current in coil PQ will flow in such a direction as to oppose the increase in magnetic flux.
   • Therefore, the induced current in coil PQ will flow in a direction such that it creates a magnetic field opposing the motion of the magnet towards the coil.
   • This means the induced current in coil PQ will flow counterclockwise when viewed from the top.

2. Coil CD:

   • As the bar magnet moves towards coil CD, the magnetic flux through the coil also increases.
   • According to Lenz's law, the induced current in coil CD will flow in such a direction as to oppose the increase in magnetic flux.
   • Therefore, the induced current in coil CD will flow in a direction such that it creates a magnetic field opposing the motion of the magnet towards the coil.
   • This means the induced current in coil CD will flow clockwise when viewed from the top.

In summary:

• The induced current in coil PQ will flow counterclockwise.
• The induced current in coil CD will flow clockwise.

To predict the polarity of the capacitor in the situation described, let's analyze the changes in magnetic flux through the loop ABCD as the magnet moves towards it.

When the magnet moves towards the loop ABCD, the magnetic flux through the loop increases. According to Faraday's law of electromagnetic induction, this increase in magnetic flux induces an electromotive force (emf) and consequently an induced current in the loop.

To oppose the increase in magnetic flux caused by the approaching magnet, the induced current will flow in such a way that it creates a magnetic field opposing the motion of the magnet towards the loop.

Using Lenz's law, we can predict the direction of the induced current in the loop. Since the magnet is moving towards the loop, the induced current will flow in a direction such that it creates a magnetic field that opposes the motion of the magnet.

Now, let's consider the capacitor in the loop ABCD. When a current flows through a capacitor, it charges the plates of the capacitor. The direction of the induced current in the loop will cause positive charge to accumulate on one plate of the capacitor and negative charge to accumulate on the other plate.

Since the induced current will create a magnetic field opposing the motion of the magnet towards the loop, the induced current will flow in such a way that it creates a magnetic field that repels the approaching magnet. This means that the induced current will generate a magnetic field that flows away from the approaching magnet.

Using the right-hand rule for the direction of the magnetic field around a current-carrying conductor, we find that the induced current will circulate counterclockwise in the loop ABCD. This counterclockwise current flow will cause positive charge to accumulate on the left plate of the capacitor and negative charge to accumulate on the right plate.

Therefore, the left plate of the capacitor will be positively charged, and the right plate will be negatively charged. This results in the polarity of the capacitor being such that the left plate is positive and the right plate is negative.