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| The potentials \(\phi_1, \phi_2, ...\) of several conductors is a linear function of charges,\(Q_1, Q_2,...,\) on the conductors. Thus \[ p_j= \sum_k p_{jk}Q_k \] Find the electrostatic energy of concentric spheres shown in figure below, having charges \(Q_1, Q_2\) by finding the matrix \(\begin{pmatrix} p_{11}, p_{12} \\ p_{21},p_{22}\end{pmatrix}\). Answer:\( \frac{1}{8\pi\epsilon_0}\Big[\Big(\frac{1}{a}-\frac{1}{b} + \frac{1}{c}\Big) Q_1^2 + \frac{2Q_1Q_2}{c} + \frac{Q_2^2}{c}\Big]\) | 09:34:29 |
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