Chapter 32, Problem 52A

Two spherical inflated rubber balloons each have the same amount of charge spread uniformly on their surfaces. If the repelling force is 2.5 N and the distance between the balloon centers is 0.30 m, find how much charge is on each balloon.

To determine

The charge on each balloon.

Answer to Problem 52A

  $q=0.5\times {10}^{-5}=5\text{μC}$

Explanation of Solution

Given:

Repelling force is 2.5 N and the distance between the balloon centers is 0.30m.

Formula used:

The force is

  $F_1=k\frac{q_1{q}_2}{{(r)}^2}$

Here,q₁and q₂are two charges.

r is the separation between them.

Calculation:

Here q₁and q₂are same. Let both has same value q.

F=2.5N and r=0.30m

Substituting the values,

  $2.5=\frac{9\times {10}^9\times q^2}{{(0.30)}^2}$

  $q^2{}_{}=\frac{2.5\times 0.09}{9\times {10}^9}$

  $q^2{}_{}=\frac{0.225}{9\times {10}^9}=0.025\times {10}^{-9}$

  $q^2=0.25\times {10}^{-10}$

  $q=0.5\times {10}^{-5}=5\text{μC}$