First slide

Electric field

Question

Two charged particles (M,+Q) and (m,-q) are placed in a gravity free space where a uniform electric field E exists. After the particles are released, they stay at a constant distance from each other. What is this distance? Neglect Gravitational interaction. k is electrostatic constant.

Moderate

A

$\sqrt{\frac{k q Q}{E (q + Q)}}$
B

$\sqrt{\frac{(M + m) k Q q}{E (q m + Q M)}}$
C

$\sqrt{\frac{(M + m) k Q q}{E (q M + Q m)}}$
D

not possible

Solution

On releasing the particles, if their acceleration is same, they will stay at a constant distance.
$\begin{array}{l} Q E - F = M a, F - q E = m a \\ where, F = \frac{k q Q}{L^{2}} \\ From above: \frac{Q E - F}{F - q E} = \frac{M}{m} \\ \Rightarrow \frac{K q Q}{L^{2}} = \frac{(m Q + q M) E}{m + M} \Rightarrow L = \sqrt{\frac{(M + m) k q Q}{E (q M + m Q)}} \end{array}$

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