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Physics question!

E

Eeezee

Diamond Member
A charged parallel-plate capacitor (effectively infinite but with a plate area A and plate separation d) is placed in a uniform magnetic field B = B*xhat. The plates are parallel to the xy plane so that the uniform electric field between the plates is E = E*zhat

a) Find the electromagnetic momentum in the space between the plates (p = mu0*eps0*E*B*A*d*yhat?)

b) Now a resistive wire is connected between the plates, along the z axis, so that th ecapacitor slowly discharges. The current through the wire will experience a magnetic force. What is the total impulse delivered to the system during the discharge? (??????)

c) Instead of turning off the electric field (as in b, suppose we slowly reduce the magnetic field. This will induce a Faraday electric field, which in turn exerts a force on the plates. Show that hte total impulse is (again) equal to the momentum originally stored in the fields. Assume the magnetic field is turned off very slowly. Thus, any induced electric field would be negligible compared to the original electric field between the plates. However, a horizontal induced electric field could not be ignored. (????????????)
 
Are you a freshman?

I've done questions like these but this will eat up some time.

edit: Oh no! its a 3D system, dammit, u can't be a freshman.

 
Eh, it's sophomore physics. Since this is obviously a homework question, I will not give the answer away. But the general idea for the last two parts is to use the Lorentz force law. Impulse is the integral of Force(t)*dt. So you should be able to use the Lorentz law to find the force generated by the current (that's the q*v cross B term I believe) or by the electric field (q*E term). Then take the time integral to find the impulse. And that's all the physics, the rest is just math (as my one of my profs would put, sure, it's easy to state out the physics when you've got the PhD).

First, your momentum is slightly wrong. Double check your equation for the momentum or the poynting vector.

This is really a great question as it ties in Maxwell's Equations in a neat demonstration. A similar question that I have had to do entails two cylindrical shells, one inside a solenoid and one outside the solenoid all sharing a common longitudinal axis.

At this point, I am going to assume that you are using Griffith's text as your problem is the same as problem 8.6. Take a look at Example 8.4, which is what I am describing.

If we give the shell inside the solenoid a charge of +Q and the exterior shell -Q, then we have an electric field between the shells that is normal to the magnetic field produced by the solenoid. So, we can exert a net torque on the shells, causing rotation, if we gradually reduce the current in the solenoid. The reason is that a changing magnetic field will induce a phi directed electric field on the inner shell. The electric field acts on the charges on the shell through Lorentz's force law and thus induces a torque. A fun problem to work out is then problem 8.7, where instead of reducing the solenoidal current, you place a wire between the two shells (neglecting the fact that it has to pass through the solenoid) which causes a current as the charges travel between the shells. The current in the wire experiences the magnetic field from the solenoid and thus experiences a force normal to it. Thus, you bring about the torque in another fashion but as we can see through electromagnetic momentum, because the field strengths at the start and end are the same, the imparted angular momentum in both cases are the same despite the different mechanisms used to create the torque.
 
For momentum, S = E*B*(1/mu0)yhat, g = eps0*E*B*yhat, p = eps0*E*B*A*d*yhat when you integrate the momentum the space between the plates. This is correct, is it not?
 
Originally posted by: Eeezee
a) Find the electromagnetic momentum in the space between the plates (p = mu0*eps0*E*B*A*d*yhat?)

...

For momentum, S = E*B*(1/mu0)yhat, g = eps0*E*B*yhat, p = eps0*E*B*A*d*yhat when you integrate the momentum the space between the plates. This is correct, is it not?
Click to expand...
No \mu_0.
 
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