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Zero Net Force Due to Like Charges

APPHEM-4KSYC6

A charge of magnitude $\mathit{Q}$ is placed at the origin. A second charge of magnitude $\mathit{2Q}$ is placed at the position $\mathit{x=d}$ along the x-axis.

Other than infinitely far away, at what position on the x-axis will a positive test charge experience a zero net force?

A

$\mathit{x=\frac{d}{\sqrt{2}}}$

B

$\mathit{x=\frac{d}{2\sqrt{2}}}$

C

$\mathit{x=\frac{d}{3}}$

D

$\mathit{x=\frac{d}{1+\sqrt{2}}}$

E

At no position other than infinitely far away will the positive test charge experience zero net force.