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In a region the electric field is E = 3y (in the y-direction, SI units). Find the total electrostatic energy stored inside a cube of side a with one corner at the origin and edges along the axes.

1. 9 a⁵ e0
2. 3 e0 a⁵
3. (3/2) e0 a⁵
4. 0

Correct answer: (3/2) e0 a⁵

Solution

With E = 3y, u = (1/2) e0 (9 y²). Integrating over the cube: U = (9 e0/2) * (a in x)(a in z) * integral of y² dy from 0 to a = (9 e0/2) a² (a³/3) = (3/2) e0 a⁵.

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