1. According to Lenz's law, the direction of induced current is such that it:
Correct Answer: c) Opposes the change in magnetic flux that produced it
Lenz's law is a consequence of the law of conservation of energy. The induced current flows in such a direction that it creates a magnetic field which opposes the change in magnetic flux that induced the current. This is why it's sometimes referred to as the "law of electromagnetic inertia."
2. When a bar magnet is moved towards a conducting loop with its north pole facing the loop, the induced current in the loop will:
Correct Answer: b) Create a south pole on the near face of the loop
When a north pole of a magnet approaches a conducting loop, the magnetic flux through the loop increases. According to Lenz's law, the induced current will flow in such a direction that it creates a magnetic field opposing this increase in flux. To oppose the approaching north pole, the near face of the loop must behave like a north pole (like poles repel). This means the current will flow in a way that creates a north pole facing the approaching magnet, making the near face of the loop effectively a north pole.
3. The negative sign in Faraday's law of electromagnetic induction ($\mathcal{E} = -\frac{d\Phi_B}{dt}$) is a mathematical representation of:
Correct Answer: b) Lenz's law
The negative sign in Faraday's law equation ($\mathcal{E} = -\frac{d\Phi_B}{dt}$) represents Lenz's law. It indicates that the induced EMF produces a current whose magnetic field opposes the original change in magnetic flux. This opposition is what Lenz's law describes.
4. A metallic ring is placed in a uniform magnetic field with its plane perpendicular to the field. If the ring is squeezed to reduce its area, the induced current will flow:
Correct Answer: a) Clockwise
When the ring is squeezed, its area decreases, causing a decrease in magnetic flux through the ring (since $\Phi_B = BA\cos\theta$, where $A$ is area). According to Lenz's law, the induced current will create a magnetic field that opposes this decrease in flux. The current will flow in such a direction that it creates a magnetic field in the same direction as the external field, trying to maintain the original flux. This direction would be clockwise when viewed from the direction of the external magnetic field.
5. Lenz's law is a consequence of which fundamental law of physics?
Correct Answer: c) Law of conservation of energy
Lenz's law is a manifestation of the law of conservation of energy. If the induced current were to flow in a direction that enhances the change in magnetic flux, it would create a self-reinforcing process that would generate infinite energy, violating energy conservation. Instead, the induced current opposes the change, requiring work to be done against this opposition, thus conserving energy.
6. A conducting loop is placed in a time-varying magnetic field. If the rate of change of magnetic flux increases, what happens to the magnitude of induced EMF?
Correct Answer: a) Increases
The magnitude of induced EMF is directly proportional to the rate of change of magnetic flux according to Faraday's law: $|\mathcal{E}| = |\frac{d\Phi_B}{dt}|$. If the rate of change of flux increases, the magnitude of induced EMF will also increase. Lenz's law only determines the direction of the induced current, not its magnitude.
7. A copper ring falls vertically through a horizontal magnetic field. During the fall, the ring experiences:
Correct Answer: c) Acceleration less than g
As the copper ring falls through a magnetic field, it cuts through magnetic field lines, inducing a current in the ring. According to Lenz's law, this induced current creates a magnetic field that opposes the motion causing it. This opposition manifests as an upward magnetic force on the ring, opposing the gravitational force. As a result, the net force on the ring is less than mg, causing it to accelerate at a rate less than g.
8. Two conducting rings are placed coaxially with a small distance between them. If a current is suddenly established in one ring, the induced current in the second ring will initially:
Correct Answer: b) Flow in the opposite direction to the first ring
When current is suddenly established in the first ring, it creates an increasing magnetic field. This changing magnetic field induces an EMF in the second ring. According to Lenz's law, the induced current in the second ring will flow in such a direction that it creates a magnetic field opposing the change. Since the magnetic field from the first ring is increasing, the induced current in the second ring will create a magnetic field in the opposite direction, which means the current flows in the opposite direction to that in the first ring.
9. A metal rod is moving with constant velocity v perpendicular to a uniform magnetic field B. The induced EMF across the ends of the rod is given by:
Correct Answer: a) $\mathcal{E} = Blv$
When a conductor of length l moves with velocity v perpendicular to a magnetic field B, the induced EMF is given by the motional EMF formula: $\mathcal{E} = Blv$. This formula is derived from Faraday's law and follows Lenz's law in terms of the direction of the induced current when the circuit is completed.
10. If a conducting loop is rotated in a uniform magnetic field about an axis perpendicular to the field, the direction of induced current:
Correct Answer: c) Reverses after every 180° rotation
When a conducting loop rotates in a uniform magnetic field, the magnetic flux through the loop changes sinusoidally: $\Phi_B = BA\cos\theta$, where $\theta$ is the angle between the field and the normal to the loop. The induced EMF is proportional to the rate of change of flux: $\mathcal{E} = -\frac{d\Phi_B}{dt}$. As the loop rotates, the flux increases and decreases, changing direction of the induced current. The direction of the induced current reverses when the rate of change of flux changes sign, which happens every 180° of rotation.