- #1
archaic
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- Homework Statement
- Determine an expression for the magnitude of the electric field at the center of any face of the cube.
- Relevant Equations
- $$E=k\frac{q}{r^2}$$
The charges at the top cancel each other's effects, and those at the bottom cancel each other's horizontal effects, so I get$$E=4k\frac{q}{r^2}\sin\theta$$I have found that ##\theta=\arcsin\left(\frac{s}{r}\right)=\arcsin{\sqrt\frac{2}{3}}##, with ##r=\sqrt{\frac{3}{2}}s##:$$E=4\frac{2}{3}\sqrt\frac23k\frac{q}{s^2}=\frac{8\sqrt6}{9}k\frac{q}{s^2}$$
Correct, right?
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