Chapter 32, Problem 50A

Consider two small charged objects, one with a charge of $15\mu C$ and the other of unknown charge. When they are separated by a distance of 1.2 m, each exerts a force of 2.8 N on the other. What is the charge of the second object?

To determine

Charge of the second object.

Answer to Problem 50A

  $q_2=300\text{μC}$

Explanation of Solution

Given:

One object has charge 15µC .

They are separated by a distance of 1.2m.

Each exerts a force of 2.8 N on the other.

Formula used:

The force between the charges is,

  $F_1=k\frac{q_1{q}_2}{{(r)}^2}$

Here,q₁and q₂are two charges and r is the separation between them.

Calculation:

Given q₁=1.5µC and r=1.2m and F=2.8N

From the coulomb’s law $F_1=k\frac{q_1{q}_2}{{(r)}^2}$

Here,k is constant, value of k is $9.0\times {10}^9 {\text{Nm}}^{\text{2}}{\text{/C}}^{\text{2}}$

  $2.8=\frac{9\times {10}^9\times 1.5\times {10}^{-6}\times q_2}{1.44}$

  $q_2=\frac{2.8\times 1.44}{9\times 1.5\times {10}^3}$

  $q_2=\frac{4.032}{13.5\times {10}^3}=0.30\times {10}^{-3}$

  $q_2=300\text{μC}$