Question

Three identical 22.0 x 10-6 Ccharges are on the corners ofan equilateral triangle of side0.111 m. Find the magnitudeof the net force on the topcharge.9291(Make sure you know the direction of each force!Remember, equilateral triangles have 60 degree interiorangles.)magnitude (N)93

Answer 1

We are given the following information.

Charge: q1 = q2 = q3 = 22.0x10-6 C

Equilateral triangle of side = 0.111 m

We are asked to find the magnitude of the net force on the top charge (q1).

The force on charge q1 due to the charge q2 is given by

$F_1=\frac{k\cdot q_1\cdot q_2}{d^2}$

Where k is the coulomb's constant (k = 9×10⁹).

$F_1=\frac{9\times10^9\cdot22\times10^{-6}\cdot22\times10^{-6}}{0.111^2}=353.54\;N$

The force on charge q1 due to the charge q3 is given by

$\begin{gathered} F_2=\frac{k\cdot q_1\cdot q_3}{d^2} \\ F_2=\frac{9\times10^9\cdot22\times10^{-6}\cdot22\times10^{-6}}{0.111^2} \\ F_2=353.54\;N \end{gathered}$

The angle between force F1 and F2 is 60°.

The resultant force on charge q1 is given by

$\begin{gathered} R=\sqrt{F_1^2+F_2^2+2F_1F_2\cos60} \\ R=\sqrt{353.54^2+353.54^2+2\cdot353.54\cdot353.54\cdot0.5} \\ R=612.35\;N \end{gathered}$

Therefore, the magnitude of the net force on the top charge is 612.35 N.