When a bar magnet is moved along the axis of a coil, it induces an electromotive force (emf) in the coil due to the change in magnetic flux. The relationship between the induced emf (e) and time (t) can be understood through Faraday's law of electromagnetic induction, which states that the induced emf in a circuit is proportional to the rate of change of magnetic flux through the circuit. To analyze this situation, let’s consider the motion of the magnet and how it affects the magnetic field around the coil. As the magnet approaches the coil, the magnetic flux through the coil increases, leading to a positive induced emf. Once the magnet is at the center of the coil, the flux reaches a maximum, and the induced emf drops to zero. As the magnet moves away from the coil, the flux decreases, resulting in a negative induced emf. Here’s a breakdown of the expected graph of induced emf versus time:

Graphical Representation of Induced EMF

The graph of induced emf (e) against time (t) can be described as follows:

• Initial Increase: As the magnet approaches the coil, the induced emf increases positively. This is because the rate of change of magnetic flux is increasing.
• Peak Value: When the magnet is at the center of the coil, the induced emf reaches its maximum value. At this point, the magnetic flux is changing at its highest rate.
• Zero Crossing: As the magnet moves past the center and begins to exit the coil, the induced emf decreases back to zero.
• Negative Induced EMF: After the magnet has completely exited the coil, the induced emf becomes negative as the flux decreases, indicating a reversal in the direction of the induced current.

Characteristics of the Graph

The resulting graph typically resembles a triangular wave, where:

• The upward slope represents the increasing magnetic flux as the magnet approaches.
• The peak represents the moment the magnet is centered.
• The downward slope indicates the decreasing flux as the magnet moves away.

Example Scenario

Imagine you are moving a bar magnet towards a coil at a steady speed. Initially, as you bring the magnet closer, the magnetic field lines through the coil increase, inducing a positive voltage. When the magnet is directly above the coil, the rate of change of the magnetic field is at its maximum, resulting in the highest induced emf. Finally, as you pull the magnet away, the induced emf reverses direction, indicating a negative voltage.

In summary, the variation of induced emf with time when a bar magnet is moved along the axis of a coil at a constant velocity is characterized by a triangular waveform, reflecting the changes in magnetic flux as the magnet approaches and then recedes from the coil. This understanding should help you identify the correct graph representation from the options provided in your question.