A bar magnet falls from rest under gravity through the center of a horizontal ring of conducting wire as shown in the figure,
Which of the following graph best represents the speed (v) vs. time(t) graph of the bar magnet?
Which of the following graph best represents the speed (v) vs. time(t) graph of the bar magnet?
The Correct Option is A
Solution and Explanation
Explanation:
1. Initial Motion:
- When the bar magnet is first released from rest, it starts to accelerate downward due to gravity.
- The speed of the magnet increases as it falls freely.
2. Induced Current and Magnetic Field:
- As the magnet approaches the ring, the changing magnetic flux through the ring induces a current in the wire (according to Faraday's Law).
- This induced current generates a magnetic field that opposes the motion of the falling magnet (Lenz's Law).
3. Deceleration:
- The opposing magnetic field creates a force that acts upward on the falling magnet, causing it to decelerate.
- The speed of the magnet decreases as it passes through the region where the magnetic flux is changing most rapidly.
4. Passing Through the Ring:
- As the magnet moves through the ring and starts to exit the other side, the rate of change of magnetic flux decreases.
- This reduces the induced current and thus the opposing magnetic force.
- The magnet starts to accelerate again, but the acceleration is less than the initial acceleration due to gravity.
5. After Passing Through the Ring:
- Once the magnet is far below the ring, the induced currents and opposing magnetic forces become negligible.
- The magnet resumes accelerating under gravity alone, but its speed is lower than it would be in free fall without the ring.
Graphical Representation:
- Option A shows:
- Initial increase in speed due to gravity.
- A dip in speed due to deceleration from the opposing force.
- A gradual increase in speed after passing the ring, but less steep.
Conclusion:
Option A correctly represents the speed vs. time graph for the magnet. So, the correct answer is option (A):
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Concepts Used:
Moving Charges and Magnetism
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Magnetism:
- The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
- And Magnetism is a property that is displayed by Magnets and produced by moving charges, which results in objects being attracted or pushed away.
Magnetic Field:
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.