Question

Two small identical balls, each of mass 0.20 g, carry identical charges and are suspended by two threads of equal lengths. The balls position themselves at equilibrium such that the angle between the threads is 60°. If the distance between the balls is 0.5 m, find the charge on each ball

Answer 1

Answer:

Hope this is the soln to this question.

Answer 2

Answer:

The charge on each ball

Explanation:

Given:

Mass, m = 0.20g

Angle, θ =$60$°

Distance between the ball, r = $0.5m$

To find:

Charge on ball, "q"

Calculation:

Coulomb's law - When two charges are separated as a distance "r"  then their force of attraction/ repulsion is directly proportional to charges and inversely proportional to distance "r".

$F = k \frac{q_{1}q_{2} }{r^{2} }$

$F = k \frac{q^{2} }{r^{2} }$                 [ two equal charges]

$F$ = $9$×$10^{-9}$×$\frac{q^{2} }{0.25}$

Now tension on the thread will be written as;

T=mg/sinθ

F=Tsinθ  ---- (1)

and T cosθ=mg  -----(2)

From equation (1) and (2) we get;

tanθ=k×q²/mgr²

q²=mgr²tanθ/k

q²=$0.20$×10×$0.25$×$9$×$10^{-9}$

q = 1.79×$10^{-7}$C

Hence charge on each ball is q = 1.79×$10^{-7}$C