Magnetic force on rotating spherical shell

In summary, Griffiths explains the reasoning for calculating the electric and magnetic forces between the hemispheres of a charged spherical shell by using the concept of average fields and spherically symmetric fields. He gives the example of an infinite plane to illustrate this concept and explains that the average field is the average of the fields inside and outside the shell. This reasoning is used to calculate the electric and magnetic forces in the problem.
  • #1
issacnewton
998
29
Hi

I was trying to do one problem from Griffiths's EM book. The problem says to find the
magnetic force of attraction between the northern and southern hemispheres of a spinning
charged spherical shell. There was an earlier problem in the book to find the electric
force of attraction between the two hemispheres of a stationary but charged spherical shell.
That was in earlier chapter. On page 103 , he gives the reasoning to calculate the electric
field to be used to calculate the force on the northern hemisphere, since the total electric
field is contributed from both the hemispheres. Giving the example of the electric field near the infinite plane, he says,

[tex] \mathbf{E}_{other}=\frac{1}{2}(\mathbf{E}_{above}+\mathbf{E}_{below}) [/tex]

and I understood the reasoning given. I have attached the two pages where he gives the explanation as png images.
Now coming to the magnetic force problem, even though he doesn't give any such reasoning
in the chapter of the Magneto-statics (chapter 5) , in the solution manual , he says that

[tex] \mathbf{B}_{avg}=\frac{1}{2}(\mathbf{B}_{in}+\mathbf{B}_{out}) [/tex]

where Bin and Bout are the magnetic fields inside
and outside of the spherical shell. I want to know where does this reasoning come from ?
 

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  • #2
Isearched on the internet, but couldn't find anything. Can someone give me someintuition where this reasoning comes from ? Thanks.The reasoning for the magnetic field is based on the fact that the magnetic field of a charged particle is spherically symmetric. This means that the average field at any given point is equal to the average of the fields inside and outside the spherical shell. This is because the field is the same in all directions from the center of the shell. So, the average field is the average of the fields inside and outside the shell.
 

1. What is the magnetic force on a rotating spherical shell?

The magnetic force on a rotating spherical shell is the force exerted on the shell due to the interaction between its rotation and a magnetic field. This force is perpendicular to both the rotation and the magnetic field.

2. How is the magnetic force on a rotating spherical shell calculated?

The magnetic force on a rotating spherical shell can be calculated using the formula F = qvBsinθ, where q is the charge of the shell, v is the velocity of the rotation, B is the strength of the magnetic field, and θ is the angle between the rotation and the magnetic field.

3. What factors affect the strength of the magnetic force on a rotating spherical shell?

The strength of the magnetic force on a rotating spherical shell is affected by the charge of the shell, the velocity of rotation, the strength of the magnetic field, and the angle between the rotation and the magnetic field. Additionally, the size and shape of the shell may also play a role.

4. Is the magnetic force on a rotating spherical shell always perpendicular to the rotation?

Yes, the magnetic force on a rotating spherical shell is always perpendicular to the rotation. This is because the magnetic force is a result of the cross product between the velocity of rotation and the magnetic field, which always results in a perpendicular force.

5. How does the magnetic force on a rotating spherical shell impact its motion?

The magnetic force on a rotating spherical shell can cause a change in the direction or speed of the shell's rotation. If the magnetic force is not balanced by other forces, it can cause the shell to accelerate or decelerate. Additionally, the direction of the magnetic force can also cause the shell to change its direction of rotation.

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