Question

Three particles, each of mass \( 1 g \) and carrying a charge \( q \), are suspended from a common point by insulated massless strings, each 100 cm long. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side length 3 cm. Calculate the charge q on each particle. (Take g = 10 m/s² ).

Answer 1

The magnitude of the forces between two charges,

\(f = \frac{1}{4\pi \in} \frac{q^2}{x^2} ; x = 3\, cm\)

The resultant electric force on any charge particle

F = 2f cos30° = √3​f.

From the geometry of the figure \(\frac{\frac{x}{2}}{y} = cos 30°\)

\(y = \frac{x}{\sqrt3}\)

Also \(\frac{y}{l} = sin \theta\)

\(\frac{\frac{x}{\sqrt3}}{y} = sin \theta\)

or \(sin \theta = \frac{3\sqrt3}{100} = \frac{\sqrt3}{100} \simeq tan \theta\)

For the equilibrium of the charge, we have

T sin θ = F

and T cos θ = mg

or tan θ = \(\frac{F}{mg}\)

After solving above equations and substituting the values, we get

q = 1.01 x 10^-7 C