Consider two infinitely large plane paralel conducting plates as shown below. The plates are uniformly charged with a surface charge density and . The force experienced by a point charge placed at the midpoint between two plates will be: [2025]

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Solution

Q.
Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+ σ$ and $- 2 σ$ . The force experienced by a point charge $+ q$ placed at the midpoint between two plates will be: [2025]

1 $\frac{σ q}{4 ε_{0}}$

2 $\frac{3 σ q}{2 ε_{0}}$

3 $\frac{3 σ q}{4 ε_{0}}$

4 $\frac{σ q}{2 ε_{0}}$

Ans.
(2)

Final charge distribution on different surfaces,

Electric field between the plates,

$E = E_{1} + E_{2} = \frac{(\frac{3}{2} σ)}{2 ε_{0}} + \frac{(\frac{3}{2} σ)}{2 ε_{0}} = \frac{3 σ}{2 ε_{0}}$

$\Rightarrow F = E q = \frac{3 σ q}{2 ε_{0}}$

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