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This is problem 3.22 from Griffiths

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We know the potential at any point on the axis perpendicular to the center of the disk, I'm asked to find the potential at any point $(r,\theta)$ assuming $r<R$ one time and $r>R$ the other.

But I'm stuck in the situation that $V$ is only specified on the axis of the disk, not on the whole boundary of my region of interest, so in this case $V$ is not specified on all the boundaries, how can I be sure it's unique?

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  • $\begingroup$ Check section 3.3 of Jackson's Classical Electrodynamics, to see the relation between the potential at the axis and the potential at any other point when you have azimuthal symmetry. After equation 3.36, this is explicitly explained. $\endgroup$ – secavara Oct 6 '19 at 12:00

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