Question

A spherical shell of radius R carries a uniform surface charge density (charge per unit area) \sigma. The center of the sphere is at the origin and the shell rotates with angular velocity \omega (in rad/sec) around the z-axis (z=0 at the origin). Seen from below, the sphere rotates clockwise. (See the figure below)

a) (a) Calculate the magnitude of the total current (in A) carried by the rotating sphere for the following values of sigma,omega and R:
sigma = 5 times 10^{-4},C/m^2, omega = 4 rad/sec and R = 1 m

b)(b) Calculate the magnitude of the magnetic field B(z) (in T) that is generated by the circular current of the rotating shell at a point P on the z-axis for the following values of sigma, omega , z and R:
sigma = 5 times 10^{-4} {C m}^{-2}, \omega = 4 rad/sec , z= 2.1 m and R =1m

Answer 1

a) I = Sigma*A*omega
b) B = mu*I/(2*(z-R))

Answer 2

Thanks!! But how to calculate A in the first part??

Answer 3

Wrong formula!!!

Answer 4

I could not get it right with that formula too.
Anonymous, is there chance that you could give us a calculated example with the above numbers?
We could trasfer it into ours, thanks.

Answer 5

Please step by step answer, I cannot figure it out too!

Answer 6

Yes, please explain the way guys!

Answer 7

Anonymous and Phy please help!

Answer 8

a) I = Sigma*A*f
f = omega/(2pi)

b) B = mu*I/(2*(z-R))

Answer 9

Anonymous, the formula is wrong. Did you get the answer right by the way?

If somebody got the answer could they provide it step by step with numbers though?

thanks