Answer:
F' = 16 F
Hence, the electric force between charges becomes sixteen times its initial value.
Explanation:
The electric force between the two charges is given by the Colomb's Law:
[tex]F = \frac{KQ_1Q_2}{R^2}[/tex] ------------------- eq(1)
where
F = electric force
K = Colomb's Constant
Q₁ = magnitude of the first charge
Q₂ = magnitude of the second charge
R = Distance between charges
Now the magnitudes of the charges are doubled and the distance between them is halved. Therefore:
[tex]F' = \frac{K(2Q_!)(2Q_2)}{(\frac{R}{2})^2}\\\\F' = 16 \frac{KQ_1Q_2}{R^2}[/tex]
using equation (1):
F' = 16 F
Hence, the electric force between charges becomes sixteen times of its initial value.
