Question

Three-point charges are arranged on a line. Charge q3 = +5.00nC and is at the origin. Charge q2 = -3.00 nC and is at x = 5.00 cm . Charge q1 is at x = 2.50 cm.What is q1 (magnitude and sign) if the net force on q3 is zero?

Answer 1

Answer:

Explanation:

Given

Charge $q_3=+5\ nC$ is placed at origin

Charge $q_2=-3\ nC$ is placed at $x=5\ cm$

Charge $q_1$ is Placed at $x=2.5\ cm$

charge $q_1$ must be positive so as to balance the force on charge $q_3$

Force on $q_3$ due to $q_1$ is

$F_{31}=\frac{kq_1q_3}{r^2}$

here $r=2.5\ cm$

$F_{31}=\frac{kq_1q_3}{(2.5)^2}$

Force on $q_3$ due to $q_2$ is

$F_{32}=\frac{kq_3q_2}{r^2}$

here $r=5\ cm$

$F_{32}=\frac{kq_3q_2}{(5)^2}$

$F_{31}=F_{32}$

$\frac{kq_1q_3}{(2.5)^2}=\frac{kq_3q_2}{(5)^2}$

$q_1=q_2(\frac{2.5}{5})^2$

$q_1=3\times (\frac{2.5}{5})^2$

$q_1=3\times \frac{1}{4}$

$q_1=0.75\ nC$