QUESTION

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An answer only to (a) will also be very helpful.


3. The quadrupole moment is given by \[ Q_{i j}=\int\left(3 x_{i} x_{j}-r^{2} \delta_{i j}\right) \rho(\vec{r}) d \tau \] Find the quadrupole moment for a. Two charges $+q$ and two charges $-q$ placed on the corners of a square in the $x-y$ plane at $\left( \pm \frac{d}{2}, \pm \frac{d}{2}, 0\right)$, such that every charge has an opposite charge for each of its neighbours. b. Four charges $+q$ and four charges $-q$ placed on the corners of a cube at $\left( \pm \frac{d}{2}, \pm \frac{d}{2}, \pm \frac{d}{2}\right)$, such that every charge has an opposite charge for each of its neighbours.

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