Answer to Question #189633 in Electricity and Magnetism for carolina

Question

Two charged spheres exert a force of 5.54 × 10^-4 N on each other. If one of the spheres has a charge of 3.72 × 10^-9 C and the other sphere has a charge of 4.32 × 10^-6 C, how far apart are the charged spheres?

Answer 1

We have given that,

Electrostatic force between two charged species = 5.54 × 10⁻⁴ N

Charge on one sphere = 3.72 × 10⁻⁹ C

Charge on other sphere = 4.32 × 10⁻⁶ C

We have to find distance between them,

We know,

$F = \dfrac{kq_1q_2}{r^2}$

$5.54 \times 10^{-4} = \dfrac{9 \times 10^9 \times 3.72 \times 10^{-9} \times 4.32 \times 10^{-6}}{r^2}$

$r^2 = \dfrac{144.6336 \times10^{-2}}{5.54}$

$r^2 = 26.107 \times 10^{-2} \\ r= \sqrt{0.26107} \\ r = 0.51m$