Answer to Question #290841 in Electricity and Magnetism for Leni

Question

Spheres A and B have the same initial positive charge qO.The magnitude of the repulsive electric force between the two spheres is 14.4 N when separated by a distance of 0.03 m.

@

a) Find the initial q0

b)The spheres are then allowed to touch each other and then separated.Find the electric force between them if the radius of sphere A is three times that of sphere B.

Answer 1

(A)F=14.4N

d=0.03m

Force

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

$14.4=\frac{9\times10^9\times q_0^2}{0.03^2}$

$1.44\times10^{-12}=q_0^2$

$q_0=1.2\times10^{-6}C$

Charge

$q_0=q_1=q_2=1.2\times10^{-6}C$

Part(b)

According to question

$\frac{q}{r}=\frac{q_0-q}{3r}$

$3q=q_0-q$

$4q=q_0$

$q=\frac{q_0}{4}$

Now force

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

$q_1=\frac{3q_0}{4},q_2=\frac{q_0}{4}$

$F=\frac{k\times\frac{3q_0}{4}\times\frac{q_0}{4}}{0.04^2}$

$$F=\frac{9\times10^9\times3\times1.2\times10^{-6}\times1.2\times10^{-6}}{16\times0.0016}=2.7N$$