Question

In the figure below, if Q = 30 mu C, and d = 30 cm, calculate the magnitude and direction of the electrostatic force on q

Answer 1

According to superimposition principle total force is vector sum of single forces thus

$\vec{F_1}=-k_c\frac{2qQ}{d^2}\hat{j}$

F2 direction is

$\theta=\arctan{\frac{d}{2d}}=26.5^{\circ}$

with respectto horizontal.

Thus

$\vec{F_2}=k_c\frac{qQ}{4d^2}\cos\theta\hat{i}-k_c\frac{qQ}{4d^2}\sin\theta\hat{j}$

Thus

$\vec{F}=k_c\frac{qQ}{4d^2}\cos\theta\hat{i}-k_c\frac{qQ}{d^2}(\frac{1}{4}\sin\theta+2)\hat{j}=3.4N\hat{i}-31.6N\hat{j}$