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. (????????????)
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. (????????????)
