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Ball in magnetic field, not understanding boundary condition

Physics Asked by Von on June 6, 2021

So I am reading solution of following exercise:

A conducting sphere with radius $R$ moves with constant velocity $v=ve_x$ inside a constant magnetic field $B=Be_y$. Find the induced charge distribution on the sphere to 1st order in $v/c$ in the laboratory inertial reference frame.
Which is on page:
https://www.physicsforums.com/threads/moving-sphere-in-magnetic-field.825426/
So the personal is this topic solves laplace equation with condition that potenial w infinity must go to $-rgamma frac{v}{c}costheta$ I don’t get why.

One Answer

Because it implements the correct boundary conditions for the electric field in the primed reference system $E'(r) to E_0vec{e}_z$. Check that this is true by taking the gradient.

Conversely you may ask what potential fulfills $nabla Phi(r,theta) = E_0vec{e}_z$ which will lead to the expression.

Admittedly, it is not obvious at first glance and the author of the question probably put some thought into it.

Answered by Nephente on June 6, 2021

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