Question

Three point charges \( -1C, +1C, +1C \) are placed at points \( A, B, C \) respectively of a triangle \( ABC \). What is the total potential energy of the system? [given \( AB = AC = 6 \, \text{cm} \) and \( BC = 3 \, \text{cm} \)]

• A. \( 0 \, J \) (Zero joule)
• B. \( 4.5 \times 10^{13} \, J \)
• C. \( 6 \times 10^{13} \, J \)
• D. \( 3 \times 10^{13} \, J \)

Hint:

For a system of point charges, calculate potential energy for each pair separately and then add all pairwise energies algebraically.

Answer 1

The Correct Option is A

Step 1: Write the formula of electrostatic potential energy.
For three point charges, total potential energy is:
\[ U = k \left( \frac{q_Aq_B}{AB} + \frac{q_Aq_C}{AC} + \frac{q_Bq_C}{BC} \right) \]

Step 2: Write the given charges.
\[ q_A = -1C, \quad q_B = +1C, \quad q_C = +1C \]

Step 3: Convert distances into metre.
\[ AB = AC = 6 \, \text{cm} = 0.06 \, \text{m} \] \[ BC = 3 \, \text{cm} = 0.03 \, \text{m} \]

Step 4: Substitute all values in the formula.
\[ U = k \left( \frac{(-1)(+1)}{0.06} + \frac{(-1)(+1)}{0.06} + \frac{(+1)(+1)}{0.03} \right) \]

Step 5: Simplify the terms.
\[ U = k \left( -\frac{1}{0.06} - \frac{1}{0.06} + \frac{1}{0.03} \right) \]
\[ U = k \left( -16.67 -16.67 + 33.33 \right) \]

Step 6: Calculate total potential energy.
\[ U = k(0) \] \[ U = 0 \, J \]

Step 7: Final Answer.
Therefore, the total potential energy of the system is:
\[ \boxed{0 \, J} \]