Understanding Induced Eddy Currents & Magnetic Retarding Force FB

[sparkle123]

I came across this in my reading and I don't understand:
How does the induced eddy current produce a magnetic retarding force F_B, and how do we know the direction of F_B?

Thanks!

 

[kuruman]

Quick answer
The eddy current can produce a magnetic force that is either retarding or accelerating the plate. If "accelerating", energy will be pumped into the system with every swing and the pendulum will be moving faster and faster in violation of energy conservation. For that reason, magnetic forces (and torques) due to induced eddy currents are like kinetic friction, they always oppose the motion.

Not so quick answer
Assume that the eddy currents are in the form of rectangular loops parallel to the sides of the plate. In what direction is the magnetic force iLxB?

 

[sparkle123]

Not so quick answer
Assume that the eddy currents are in the form of rectangular loops parallel to the sides of the plate. In what direction is the magnetic force iLxB?

But L (direction of current) is in a circle, so the force vectors are in a circle and cancel each other out?
Like the force due to the current in the ascending part of the loop cancels the force due to the current in the descending part of the loop...

Thanks!

 

[kuruman]

You don't know that it is a circle. The drawing is just a schematic to show the clockwise or counterclockwise circulation of the current. Suppose that instead of rectangular plate you had a rectangular loop made from very thin wire swinging in the field. What would the magnetic forces look like then? Would they be different from a filled plate? Look at the plate as a whole lot of nested rectangular loops, one slightly smaller than the other.

*** On edit ***
Of course, if the loop is entirely in the region of uniform field, the net force will be zero as you say. However, there will be an unbalanced retarding force when only part of the loop is in the region of magnetic field. That's why the figure in the textbook looks they way it does.

 

[sparkle123]

Thanks! I still don't understand though...
using the right hand rule we have the fingers going into the page following B, and the force is the palm, so the thumb should point up, so L is in the upward direction? Why?

Does counterclockwise/clockwise not matter then? I notice that the right plate is clockwise but the force is still to the left.

 

[kuruman]

Thanks! I still don't understand though...
using the right hand rule we have the fingers going into the page following B, and the force is the palm, so the thumb should point up, so L is in the upward direction? Why?

Using the right hand rule on what part of the circuit? If you view the plate as a rectangular wire, there are four sides each with its own magnetic force acting on it.

Does counterclockwise/clockwise not matter then? I notice that the right plate is clockwise but the force is still to the left.

Sure it matters. Reversing the direction of the current reverses all forces. The clockwise current that we see from our side of the screen becomes a counterclockwise current to someone looking at the pendulum from behind the screen. Yet we both agree that the force opposes the motion.

Look at the plate on the left in the drawing. Assume that it is a wire loop along the edges of the rectangle. The top and bottom (short) pieces contribute forces that are canceled by the support. Of the remaining two (long) sides, only the one that is inside the field region contributes an iLxB force. What is the direction of that force?

 

[sparkle123]

OH I get it! Thanks so much! :)