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Strength of Electrostatic Force

There are two...

Question

There are two unknown charges, $Q_{1}$ and $Q_{2}$ . A positive charge is placed at P. P is closer to $Q_{2}$ than $Q_{1}$ . If the net electric force acting on the charge at P is zero, then conclusion is :

A

Both

Q_{1}

and

Q_{2}

are positive

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B

Both

Q_{1}

and

Q_{2}

are negative

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C

Both

Q_{1}

and

Q_{2}

have opposite signs

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D

Both

Q_{1}

and

Q_{2}

have the same sign, but the magnitude of

Q_{1}

is greater than the magnitude of

Q_{2}

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E

Q_{1}

and

Q_{2}

have same sign, but the magnitude of

Q_{2}

is greater than the magnitude of

Q_{1}

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Solution

The correct option is D Both $Q_{1}$ and $Q_{2}$ have the same sign, but the magnitude of $Q_{1}$ is greater than the magnitude of $Q_{2}$
The net force on charge q at P is zero if force on charge at P due to $Q_{1}$ is equal to force on charge at P due to $Q_{2}$
i.e, $\frac{k q Q_{1}}{r_{1}^{2}} = \frac{k q Q_{2}}{r_{2}^{2}}$ where $r_{1} =$ distance from P to $Q_{1}$ and $r_{2} =$ distance from P to $Q_{2}$
or, $Q_{1} = Q_{2} \frac{r_{1}^{2}}{r_{2}^{2}}$
Thus, both $Q_{1}$ and $Q_{2}$ have same sign and since $r_{1} > r_{2}$ , so $Q_{1}$ is greater than the magnitude of $Q_{2}$

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