Lenz's law: Current induced in a split loop by a changing B-field

[subhradeep mahata]

Homework Statement

We have a circular loop of wire, with AB is another wire which is also the diameter of the circular loop. The direction of magnetic field is perpendicular to the loop, into the plane of paper. The magnetic field strength is decreased at a constant rate, without changing the direction.What is the direction of current incuced in the wire AB, if any?

Homework Equations

The Attempt at a Solution

As magnetic field is into the plane of paper, and decreasing at a constant rate, it is obvious that current in the loop will be in the clockwise direction. But, I am not sure whether current will be passed in the wire AB. Also, the question seems to be a bit incorrect/incomplete to me, so feel free to ask me for any assumptions.See is you can help me out.

 

[ehild]

Homework Statement

We have a circular loop of wire, with AB is another wire which is also the diameter of the circular loop. The direction of magnetic field is perpendicular to the loop, into the plane of paper. The magnetic field strength is decreased at a constant rate, without changing the direction.What is the direction of current incuced in the wire AB, if any?
View attachment 233567

Homework Equations

The Attempt at a Solution

As magnetic field is into the plane of paper, and decreasing at a constant rate, it is obvious that current in the loop will be in the clockwise direction. But, I am not sure whether current will be passed in the wire AB. Also, the question seems to be a bit incorrect/incomplete to me, so feel free to ask me for any assumptions.See is you can help me out.

Both half circles with the wire AB constitute closed paths, and the changing magnetic flux produces emf in both. What currents flow in the half circles?

 

[osilmag]

There wouldn't be much induced in AB since its plane is not perpendicular to the magnetic field.

 

[ZapperZ]

There wouldn't be much induced in AB since its plane is not perpendicular to the magnetic field.

AB is not a plane. It is a line. But AB connected to the rest of the loop forms its own loop/s, and thus, forming a plane, which in this case, is definitely perpendicular to the magnetic field.

Zz.

 

[subhradeep mahata]

@ehild In both the half circles, clockwise current will be set up. In the upper half circle, current direction is from B to A and in the lower one it is from A to B, the current magnitude being same in both the cases. So, i think clockwise current will be set up in the overall circular loop, with no current going in wire AB.

 

[ehild]

@ehild In both the half circles, clockwise current will be set up. In the upper half circle, current direction is from B to A and in the lower one it is from A to B, the current magnitude being same in both the cases. So, i think clockwise current will be set up in the overall circular loop, with no current going in wire AB.

Correct.

 

[subhradeep mahata]

@ehild Thanks.