Physics 341 HW 32
Due Monday, 11 December 2017
1. In our second in-class example, suppose that instead of turning off the magnetic field by reducing the current in the solenoid, we instead attach weakly conducting spokes between the charged cylinders that allow both cylinders to slowly become neutral, reducing the electric field between them to zero (while keeping the magnetic field constant).
a) Determine the magnetic field between the cylinders induced by the changing electric field.
b) Determine the Lorentz force on the current in the weakly conducting spokes.
c) Use your expression from b to determine the total change in angular momentum in the cylinders, and compare this to what we got in class where we turned off the magnetic field.
2. Two concentric spherical shells carry uniformly distributed charges +Q (inner shell radius a) and –Q (outer shell radius b). They are put into a uniform magnetic field B=Bo z.
a) Determine the angular momentum in the fields (with respect to the center of the spheres).
b) Now the magnetic field is gradually turned off. Find the torque on each sphere and the resulting angular momentum of the system.
Physics 341 HW 32
Due Monday, 11 December 2017
1. In our second in-class example, suppose that instead of turning off the magnetic field by reducing the current in the solenoid, we instead attach weakly conducting spokes between the charged cylinders that allow both cylinders to slowly become neutral, reducing the electric field between them to zero (while keeping the magnetic field constant).
a) Determine the magnetic field between the cylinders induced by the changing electric field.
b) Determine the Lorentz force on the current in the weakly conducting spokes.
c) Use your expression from b to determine the total change in angular momentum in the cylinders, and compare this to what we got in class where we turned off the magnetic field.
2. Two concentric spherical shells carry uniformly distributed charges +Q (inner shell radius a) and –Q (outer shell radius b). They are put into a uniform magnetic field B=Bo z.
a) Determine the angular momentum in the fields (with respect to the center of the spheres).
b) Now the magnetic field is gradually turned off. Find the torque on each sphere and the resulting angular momentum of the system.