Calculate the force of magnetic attraction between the northern and southern hemispheres of a uniformly charged spinning spherical shell, with radius R, angular velocity ω, and surface charge density σ. [This is the same as Prob. 5.44, but this time use the Maxwell stress tensor and Eq. 8.21.]

Solution 3P

Step 1 of 5</p>

To find the magnetic force of attraction between the northern and southern hemisphere for a charged spherical spinning sphere shell with radius ‘R’ and angular velocity .

Step 2 of 5</p>

The Maxwell’s tensor equation is given by;

….(1)

And, we have if indices are same, and for E = 0

Let us consider the Maxwell’s stress tensor which is given by,

….(2)

Now, let us calculate the force for the upper charge for the xy-plane , E = 0, we have;

and we know that,

So, from eq(1) we get,

….(3)

Step 3 of 5</p>

Let us consider the magnetic field across the shell, since the magnetic field is discontinuous across the shell we have,

for r < R ….(4)

Where ‘R’ is the radius of the sphere, is the angular speed and is the surface charge density