Electrostatic Force Between Two Charges - Interactive Quiz

Electrostatic Force Between Two Charges [Kerala PET 2012]

Question: Two equal point charges each of \( 3\mu C \) are separated by a certain distance in meters. If they are located at \( ( \hat{i} + \hat{j} + \hat{k} ) \) and \( ( 2\hat{i} +3\hat{j} +3\hat{k} ) \), then the electrostatic force between them is:

Select the Correct Option

(a) \( 9 \times 10^3 \) N

(b) \( 9 \times 10^{-3} \) N

(c) \( 10^{-3} \) N

(d) \( 9 \times 10^{-2} \) N

Detailed Step-by-Step Solution

Step 1: Calculate the distance \( r \) between the two charges using the distance formula:

\( r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \)

Given points:
\( A(1,1,1) \) and \( B(2,3,3) \)

\( r = \sqrt{(2-1)^2 + (3-1)^2 + (3-1)^2} \)
\( = \sqrt{1 + 4 + 4} \)
\( = \sqrt{9} = 3 \) meters

Step 2: Use **Coulomb's Law** to calculate the electrostatic force:

\( F = \frac{k q_1 q_2}{r^2} \)

Where:
\( k = 9 \times 10^9 \) (Coulomb's constant),
\( q_1 = q_2 = 3 \times 10^{-6} C \),
\( r = 3 \) m

\( F = \frac{(9 \times 10^9) \times (3 \times 10^{-6}) \times (3 \times 10^{-6})}{(3)^2} \)
\( = \frac{(9 \times 10^9) \times (9 \times 10^{-12})}{9} \)
\( = 9 \times 10^-3 \) N

Final Answer: The electrostatic force between the charges is **\( 9 \times 10^-3 \) N.