Question

Suppose you wanted to increase the force between two point charges by a factor of 5. By what factor must you change the distance between them

Answer 1

Answer:

the distance between the two point charges will be reduced by a factor of  $\frac{1}{\sqrt{5} } = 0.447$

Explanation:

The force between two point charges is given by Coulomb's law;

$F = \frac{kQ_1Q_2}{r^2}$

where;

k is Coulomb's constant

Q₁ and Q₂ are two point charges

r is the distance between the two charges

From the equation above, the following relationship between force and distance can be deduced;

F₁r₁² = F₂r₂²

F₁r₁² = (5F₁)r₂²

r₁² = 5r₂²

$r_2^2 = \frac{r_1^2}{5} \\\\r_2 = \sqrt{\frac{r_1^2}{5}} \\\\r_2 = \frac{r_1}{\sqrt{5} } \\\\r_2 = \frac{1}{\sqrt{5} } \ r_1\\\\r_2 = 0.447( r_1)$

Thus, the distance between the two point charges will be reduced by a factor of  $\frac{1}{\sqrt{5} } = 0.447$