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Question

If the force between two charges is 9N, what will be the force if the distance between them is doubled and both the charges are increased to sqrt(2) times? 9N 4.5N 3N 3.75N Other:SHOW LESS0

Solution

18N.

Step 1: Let's denote the initial force as F, the initial distance between the charges as d, the initial charge as q, and the initial force constant as k. Therefore, we have: [ F = \dfrac{k \cdot q^2}{d^2} ]

Step 2: If the distance is doubled and both charges are increased to $$\sqrt{2}$$ times, the new force F' can be calculated as: [ F' = \dfrac{k \cdot (2q\sqrt{2})^2}{(2d)^2} ] [ F' = \dfrac{k \cdot 8q^2}{4d^2} ] [ F' = 2 \cdot \dfrac{k \cdot q^2}{d^2} ] [ F' = 2F ]

Step 3: Therefore, if the distance between the charges is doubled and both charges are increased to $$\sqrt{2}$$ times, the new force will be twice the initial force. Explanation: When the distance between the charges is doubled and both charges are increased to $$\sqrt{2}$$ times, the force between them will be doubled due to the inverse square law of electric force.

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