First slide

Electrostatic force

Question

Two point charges $+ 3 μ C$ and $+ 8 μ C$ repel each other with a force of 40 N. If a charge of $- 5 μ C$ is added to each of them, then the force between them will become

Moderate

A

- 10 N
B

+10 N
C

+ 20 N
D

- 20 N

Solution

$Here, F = 40 = \frac{k (3) (8)}{r^{2}} = \frac{24 k}{r^{2}}$
$and F^{'} = \frac{k (3 - 5) (8 - 5)}{r^{2}} = \frac{k (- 2) (3)}{r^{2}} = \frac{- 6 k}{r^{2}}$
$\begin{array}{l} ∵ \frac{F^{'}}{F} = \frac{- 6 k}{r^{2}} \times \frac{r^{2}}{24 k} = - \frac{1}{4} \\ \Rightarrow F^{'} = - \frac{F}{4} = - \frac{40}{4} = - 10 N \end{array}$

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