Answered

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What happens to the force between two charges when each charge is doubled and the distance between them is 1/4 its original
magnitude?

Sagot :

Answer:

F' = 64 F

Explanation:

The electric force between charges is given by :

[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]

Where

q₁ and q₂ are charges

r is the distance between charges

When  each charge is doubled and the distance between them is 1/4 its original magnitude such that,

q₁' = 2q₁, q₂' = 2q₂ and r' = (r/4)

New force,

[tex]F'=\dfrac{kq_1'q_2'}{r'^2}[/tex]

Apply new values,

[tex]F'=\dfrac{k\times 2q_1\times 2q_2}{(\dfrac{r}{4})^2}\\\\=\dfrac{k\times 4q_1q_2}{\dfrac{r^2}{16}}\\\\=64\times \dfrac{kq_1q_2}{r^2}\\\\=64F[/tex]

So, the new force becomes 64 times the initial force.

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