What happens to the force between two point charges if the separation between them is doubled

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If the distance between two charged particles is doubled, the strength of the electric force between them will __________.

Possible Answers:

Correct answer:

be quartered

Explanation:

Coulomb's law gives the relationship between the force of an electric field and the distance between two charges:

The strength of the force will be inversely proportional to the square of the distance between the charges.

When the distance between the charges is doubled, the total force will be divided by four (quartered).

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Text Solution

Solution : From Coulombs law, `F prop 1/d^(2)`. So <br> (a) When distance is reduced to half, force increases by four times. `[ :' F_(2)=(F_(1)d_(1)^(2))/((d_(1)/2)^(2))=4F_(1)]` <br> (b) When distance is doubled, then force is reduced by four times. `[ :' F_(2)=(F_(1)d^(2))/(|2d_(1)|^(2))=1/4 F_(1)]`