Question

In the figure particle 1 of charge q1-1.04 HC and particle 2 of charge a2- -2.98 uC, are held at separation L-9.5 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a)x and (bly coordinates of particle 3? (a) Number Units (b) Number Units

Answer 1

The electric force on charge 3 cannot be zero, if it is placed between the two charges 1 and 2.Since charge 1, $q_1=1.04\,\mu C$ is positive and charge 2 , $q_2=-2.98\,\mu C$ is negative.

The unknown charge $q_3$ either positive or negative must be placed to the left of  the charge $q_1=1.04\,\mu C$ (smaller)

Charge $q_3$ is placed at a distance of $x$ to the left of charge $q_1$ and at a distance of $x+L$ from $q_2$

Net electrostatic force on charge 3 is ${F}_{31}+{F}_{32}=-\frac{kq_1q_3}{x^2}+\frac{kq_2q_3}{(x+L)^2}=0$

$\frac{q_1}{x^2}=\frac{q_2}{(x+L)^2}$

${q_1}{(x+L)^2}=q_2x^2$

${1.04\mu}\,{(x+9.5)^2}=2.98\,\mu \, x^2$

${(x+9.5)^2}=2.865 \, x^2$

$x^2+19x+90.25=2.865 \, x^2$

$-1.865x^2+19x+90.25=0$

$x=13.72\,cm$ to the left of charge 1.

If the charge $q_1$ is at origin (0,0), then charge $q_3$ is placed at $(-13.72\,cm,0\,cm)$

a) X-coordinate of particle 3 is $-13.72\,cm$

b) Y-coordinate of particle 3 is $0\,cm$