Calculating Resistance of a Steel Ball in Spherical Coordinates

[player1_1_1]

Homework Statement

hello, how can i count resistance of a ball (i mean ball ex. steel ball, not other) which is connected with battery by wires in spherical coordinates: A_1=(R,\theta_1,\phi_1),A_2=(R,\theta_2,\phi_2)? it would be easy if they were antipodes, then i would just integrate \mbox{d}R=\rho\frac{\mbox{d}l}{S(l)} but what to do in this case?

 

[sigmaro]

i coulndt solve your problem but i may help you do
these are not trifling tricks, you must be dealing with vector calculus, and it is quite dangerous and advanced.
now, when they were at antipodes, for each disk on the way you were having a constant dV/dx and so E and multipling it with sigma you were having J and multipling it with dA you were having I and R was simply V/I
now, here you have to somehow find distribution of V and gradient(V)=E and the rest is easy but how on the Earth we can find that distribution. i propose a modal let's consider position of V1 is a, V2 is b and for an arbitrary d points voltage would be V=(V2-V1)(d-a)/[(d-a)+(d-b)] that works when reducting to our simple old pole-to-pole question but i am not sure for this case, please if you find solition share it here. (btw the substractions are vectoral there but summation is scalar!) even if this is the potantial difference i can't even dare to mathematics
sorry about not giving a proper answer but it has really been a long time
thanks for the question