Question

Two stacked rings have currents in opposite directions as shown. There is a net magnetic force exerted on the top ring due to the bottom ring. Is which direction is this force?

		to the right
		to the left
		downward
		upward
		The net force is zero.

Answer 1

We have two rings carrying currents in opposite direction, with one ring stacked on other.

In our case for finding the direction of magnetic force on the top ring due to bottom ring, Consider without any loss of generality , top ring carries current in the anticlockwise direction and bottom ring carries current in the opposite direction that is in clockwise direction.

Now we will use right hand thumb rule for the direction of magnetic field at the center of both rings.

As per right hand thumb rule if we curl our fingers of right hand in the the direction of flow of current through the ring and stretch the thumb outward so as to form the thumbs up (or thumbs down) sign with the right hand, the stretched thumb of our right hand will point in the direction of magnetic field at the center of the ring.

Now in case of top ring as per right hand thumb rule if we curl our fingers of right hand anticlockwise in the direction of flow of current throgh top ring, our stretched thumb of right hand will point upward, implying magnetic field at the center of the top ring is directed upward.

This implies surface bottom area (surface area bound by the ring) through which the magnetic field lines enter the surface area of the top ring acts as a magnetic South pole and upper surface area through which the magnetic field lines leave the surface area of the top ring acts as a manetic North pole

Similarly in case of bottom ring as per right hand thumb rule if we curl finger of right hand clockwise in the direction of flow of current theough bottom ring, our stretched thumb of right hand will point downward, implying that magnetic field at the center of the bottom ring is directed downward.

Similarly as mentioned one paragraph above this implies upper surface area of the bottom ring acts as a magnetic south pole and bottom surface area acts as a magnetic North pole.

Now remeber two same poles of magnets repell each other.

Now in our case for two given current carrying rings acting as magnets, South magnetic pole (bottom surface area) of the top ring will be repelled by the South magnetic pole (top surface area) of the bottom ring, that is bottom ring is pushing upward on top ring.

That is repulsive magnetic force exerted by the bottom ring on top ring is directed downward.

So the answer is,

Net magnetic force exerted on top ring due to the bottom ring is directed upward.

(Remember as mentioned above the answer will not depend on in exactly which direction the currents are flowing through given rings as long as they are carrying currents in opposite direction with respect to each other.)