Question

A vertical bar magnet is dropped through the center of a horizontal loop of wire, with its north pole leading. At the instant when the midpoint of the magnet is in the plane of the loop, the induced current in the loop, viewed from above, is:

Answer 1

Answer:

When the midpoint of the magnet is in the plane of the loop, the induced current in the loop viewed from above is essentially zero.

Explanation:

At some point far away from the plane of the loop of the wire, there's no flux and hence, no induced emf, and no current in the loop. As the magnet descends and gets close to the entrance of the coil, some of the magnetic field from the magnet threads the top few imaginary disks of the coil. The time changing flux induces some EMF and subsequently some induced current.

As the magnet continues to fall, and enters the coil, more of its magnetic field is threading imaginary disks in the coil, so as it moves, the time rate of change of total flux increases, so the EMF goes up. Note that the field lines above and below the magnet's midpoint point in the same direction from the the North pole to the south.

As the bar moves through the plane of the coil, the North end first, flux is added by the motion of the magnet and flux is removed by the motion of South end.

At some point, the bar reaches the middle of the coil. At this point, the amount of flux added to the top half of the coil by a small motion of the magnet is equal to the amount of flux removed from the bottom half. Therefore, at this point the EMF is zero. And hence, there is no induced current observed in the wire at this point.

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Answer 2

When viewed from the above, there is no induced current observed in the wire at this point due to zero EMF.

The given problem is based on the concept of electric flux and induced emf. The electric flux is dependent on induced emf, which is produced to current. Since,  point far away from the plane of the loop of the wire, there's no flux and hence, no induced emf, and no current in the loop.

• As the magnet descends and gets close to the entrance of the coil, some of the magnetic field from the magnet threads the top few imaginary disks of the coil. The time changing flux induces some EMF and subsequently some induced current.

• When magnet continues to fall, and enters the coil, more of its magnetic field is threading imaginary disks in the coil, so as it moves, the time rate of change of total flux increases, so the EMF goes up.

Note: - The field lines above and below the magnet's midpoint point in the same direction from the the North pole to the south.

• As the bar moves through the plane of the coil, the North end first, flux is added by the motion of the magnet and flux is removed by the motion of South end.

• When the bar reaches the middle of the coil, then at this point the amount of flux added to the top half of the coil by a small motion of the magnet is equal to the amount of flux removed from the bottom half. Therefore, at this point the EMF is zero. And hence, there is no induced current observed in the wire at this point.

Thus, we conclude that when viewed from the above, there is no induced current observed in the wire at this point due to zero EMF.

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