Answer to Question #280228 in Electricity and Magnetism for Anonymous005

Question

1. a Calculate the force between two charges q1 of

2.0 μC and q2 4.0 μC separated by r = 5.0 cm. (Ans: 29 N)

b Let the force calculated in a be F. In terms of F

and without further calculations, state the force

between these charges when:

i the separation r of the charges is doubled (Ans: F/4)

ii q1 and r are both doubled (F/2)

iii q1, q2 and r are all doubled. (F)

Please explain how these problems were solved.

Answer 1

(a)

Force

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

$$F=\frac{9\times10^{9}\times2\times10^{-6}\times4\times10^{-6}}{0.05^2}=28.8N \\F=28.8N \\ (approximately F=29N)$$

(1)

Force

$F=\frac{kq_1q_2}{r_1^2}$

$r_1=2r$

$F=\frac{kq_1q_2}{(2r)^2}=\frac{F}{4}$

(2)

$F=\frac{kq_1q_2}{r_1^2}$

$q_1=2q_1,r=2r$

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

(3)

$F=\frac{kq_1q_2}{r_1^2}$

$q_1=2q_1,q_2=2q_2,r=2r$

$F=\frac{k2q_12q_2}{(2r)^2} \\F=\frac{4kq_1q_2}{4r^2}=F$

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