First slide

Electrostatic force

Question

Two identical charges, $5 μ C$ each, are in the air. What is the largest charge to be transferred from one charge to another, so that their interaction force decreases to 2.5 times?

Moderate

A

$\sqrt{11} μ C$
B

$4 μ C$
C

$\sqrt{13} μ C$
D

$\sqrt{15} μ C$

Solution

Given
Charge $q = 5 μC$
Let Q $μ C$ is transferred from one charge to other.
We know coloumb force $F = \frac{k q^{2}}{r^{2}} ..... (1)$
$\Rightarrow \frac{k \times {(5 \times 10^{- 6})}^{2}}{r^{2}} = 2.5 \times \frac{k (5 - Q) (5 + Q)}{r^{2}}$
$\Rightarrow \frac{{(5 \times 10^{- 6})}^{2}}{2.5} = (5 - Q) (5 + Q) \times 10^{- 12}$
$\Rightarrow \frac{25 \times 10^{- 12}}{2.5} = (25 - Q^{2}) \times 10^{- 12}$
$∴ Q = \sqrt{15} μC$

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