Question:
Figure shows a triangular array of three point charges. The electric potential \( V \) of these source charges at the midpoint \( P \) of the base of the triangle is:
Figure shows a triangular array of three point charges. The electric potential \( V \) of these source charges at the midpoint \( P \) of the base of the triangle is:
Show Hint
The electric potential is a scalar quantity, so you sum the potentials from each charge algebraically.
Updated On: Apr 28, 2026
- 55 kV
- 63 kV
- 45 kV
- 48 kV
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Formula for electric potential
Electric potential at a point due to multiple point charges is:
\[ V = \frac{1}{4\pi\epsilon_0} \sum \frac{q_i}{r_i} \]
Step 2: Identify contributions
Each charge contributes potential based on its magnitude and distance from point P:
\[ V = k\left(\frac{q_1}{r_1} + \frac{q_2}{r_2} + \frac{q_3}{r_3}\right) \] where \(k = \frac{1}{4\pi\epsilon_0}\)
Step 3: Substitution (geometry dependent)
Substituting the given charge values and their respective distances (as provided in the question diagram):
\[ q_1 = 1\times10^{-6}C,\quad q_2 = 3\times10^{-6}C,\quad q_3 = -2\times10^{-6}C \] After substituting distances and simplifying:
\[ V = 6.3 \times 10^{4}\ V \]
Final Answer:
\( V = 63\ \text{kV} \)
Electric potential at a point due to multiple point charges is:
\[ V = \frac{1}{4\pi\epsilon_0} \sum \frac{q_i}{r_i} \]
Step 2: Identify contributions
Each charge contributes potential based on its magnitude and distance from point P:
\[ V = k\left(\frac{q_1}{r_1} + \frac{q_2}{r_2} + \frac{q_3}{r_3}\right) \] where \(k = \frac{1}{4\pi\epsilon_0}\)
Step 3: Substitution (geometry dependent)
Substituting the given charge values and their respective distances (as provided in the question diagram):
\[ q_1 = 1\times10^{-6}C,\quad q_2 = 3\times10^{-6}C,\quad q_3 = -2\times10^{-6}C \] After substituting distances and simplifying:
\[ V = 6.3 \times 10^{4}\ V \]
Final Answer:
\( V = 63\ \text{kV} \)
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