Two spherical conductors B and C having equal | vedclass

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Question

Let the spherical conductors $B$ and $C$ have same charge as $q$.

The electric force between them is

$\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}}

Vedclass · Accepted Answer

$\frac{3F}{8}$

Vedclass · Answer

Let the spherical conductors $B$ and $C$ have same charge as $q$.

The electric force between them is

$\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{2}}$

$r,$being the distance between them. When third uncharged conductor $A$ is brought

in contact with $\mathrm{B}$, then charge on each conductor

$q_{A}=q_{B}=\frac{q_{A}+q_{B}}{2}=\frac{0+q}{2}=\frac{q}{2}$

When this conductor $A$ is now brought in contact with $C$, then charge on each conductor

$q_{A}=q_{C}=\frac{q_{A}+q_{C}}{2}=\frac{(q / 2)+q}{2}=\frac{3 q}{2}$

Hence, electric force acting between $\mathrm{B}$ and $\mathrm{C}$ is

$\mathrm{F}^{\prime}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{B} q_{C}}{r^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{(q / 2)(3 q+4)}{r^{2}}$

$=\frac{3}{8}\left[\frac{q}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{2}}\right]=\frac{3 F}{8}$

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