# Energy

## Homework for Symmetries

1. (EnergyGEM231)

Three charges are situated at the corners of a square (side $s$). Two have charge $-q$ and are located on opposite corners. The third has charge $+q$ and is opposite an empty corner.

1. How much work does it take to bring in another charge, $+q$, from far away and place it at the fourth corner?

2. How much work does it take to assemble the whole configuration of four charges?

2. (SquareHoopGEM24)

Consider a square loop with each side length $a$ carrying a uniform linear charge density $\lambda$.

1. Find the electric field a distance $z$ above the center of the square. (You may start with the electric field due to a single finite line of charge).

2. Find the work needed to bring a charge in from infinity along the $z$-axis.

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