Question

Three equal charges of +10 nC are located at the corners of an equilateral triangle whose sides are 10 cm long. What is the magnitude of the force experienced by each charge due to the others?

Phys 2: steps are much appreciated, thanks!

Answer 1

10nC Q2 Q1 10nC

Calculate the forces between any two charges

$\large F=\frac{1}{4\pi \epsilon _0}\frac{Q_1Q_2}{r^2}$

$\large F=k\frac{Q^2}{r^2}$   as we know here $\large Q_1=Q_2=Q=10nC=10\times 10^{-9}C$

$\large k=9\times 10^9Nm^2C^{-2}$

Two forces are applied at each corner with a $\large 60^0$ angle between them

the resultant force at each corner,

$\large F_{Resultant}= 2Fcos30 ^0$

$\large F=\frac{9\times 10^9\times (10\times 10^{-9})^2}{(10\times 10^{-2})^2}$

$\large F=\frac{9\times 10^9\times (100\times 10^{-18})}{0.01}=9.0 \times 10^{-5}N$

$\large F_{Resultant}= 2\times 9.0\times 10^{-5}cos30 ^0$

$\large F_{Resultant}= 15.588\times 10^{-5}N$