A spherical sheet of radius a has surface-charge density which depends on the po

Question

A spherical sheet of radius a has surface-charge density which depends on the polar angle according to the formula:

where 0 and 1 are constants. Find a) the total charge, and b) the dipole moment. Use z = r cos. FIrst explain how symmetry imples that Qtotal is determined only by 0, and px = py = 0, and pz is determined only by 1; no mathematical proofs are needed here!!

Please, I need to see work!! I need to understand how to get the solution. I will reward you if you give a detailed explaination! <3

Explanation / Answer

o(0)=o_0+o_1*cos(theta). dQ=o(theta)*ds=o(theta)*dtheta*a^2*sin(theta)*2pi. so dQ=(o_0+o_1*cos(theta))*sin(theta)*dtheta*a*2pi integrate from theta = 0 to theta = 180. so Q=o_0*2*a^2*2pi -------------------- b). you can see that charge is distributed "surround" z-axis. so Px=Py now you can see that because with the same theta, the charge density is the same, so each small magnetic dipole is zero. so Px=Py=0. ---- now in z-axis. o_0 not realate because this o_0 charge density tend to make charge distributed uniformly, so its "dipole" is zero also (because of it is uniform)

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