Quick induced current from magnetic field question direction of current?

[michaelw]

With RHR-1, if the rod moves to the right in a field coming into the page, the force will move positive charge up (in reality move negative electrons down) in the rod, and induce a current
but why is the current counter clockwise?

 

[Gokul43201]

There are two ways to answer what I think is your question.

1) Think of the Lorentz force on a charge in a magnetic field, \vec{F} = q(\vec{v} \times \vec{B}). Using the RHR tells you that the force acts upwards along the rod, making the current want to go up the rod and hence counter-clockwise. Taking this a step further, this Lorentz force merely results from an electric field that is set up in a moving conductor in a B-field. This electric field set up across the rod propagates through the rest of the loop, forcing the current to travel in the required direction.

2) Think of Lenz's Law. The current will be set up in the loop in a manner that attempts to counter its cause. The cause in this case, is the increasing flux (B.A) enclosed within the loop as the rod moves to the right. Hence, the current will go in a direction that will try to reduce this flux. So naturally, the current wants to induce a magnetic field in a direction opposite to the existing field. Again, you can use the right hand thumb rule to tell that it takes a counterclockwise current to induce a field coming out of the plane of the paper.

 

[thepatientmental]

The direction of the induced current can be determined using the Right Hand Rule (RHR-1) for electromagnetic induction. According to this rule, if the rod is moving to the right in a magnetic field that is coming into the page, the force on the positive charge will be upwards. This means that the positive charge will move in a direction perpendicular to both the direction of motion and the magnetic field.

Since the force on the positive charge is upwards, the direction of the induced current will be counterclockwise. This is because the direction of the current is always opposite to the direction of the force on the positive charge, as per the RHR-1. Therefore, the negative electrons in the rod will actually move in a downward direction, but the overall current will be counterclockwise.

In summary, the direction of the current is determined by the direction of the force on the positive charge, which is perpendicular to both the direction of motion and the magnetic field. This is why the current is counterclockwise in this scenario.