Question:
$A$, $B$ and $C$ are three points in space forming an equilateral triangle of side $10$ cm. If a point charge $8\,\mu C$ is placed at $A$, then the work done in moving a unit charge from $B$ to $C$ is
$A$, $B$ and $C$ are three points in space forming an equilateral triangle of side $10$ cm. If a point charge $8\,\mu C$ is placed at $A$, then the work done in moving a unit charge from $B$ to $C$ is
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If two points are at equal distance from a charge:
- Their potentials are equal
- No work is required to move charge between them
Updated On: Apr 30, 2026
- zero
- $720$ J
- $7200$ J
- $360$ J
- $3600$ J
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The Correct Option is A
Solution and Explanation
Concept:
Work done in moving a charge depends on potential difference:
\[
W = q(V_B - V_C)
\]
Potential due to a point charge:
\[
V = \frac{kQ}{r}
\]
Step 1: Find distances from charge at $A$.
Since $ABC$ is an equilateral triangle: \[ AB = AC \]
Step 2: Compare potentials at $B$ and $C$.
\[ V_B = \frac{kQ}{AB}, \quad V_C = \frac{kQ}{AC} \] \[ AB = AC \Rightarrow V_B = V_C \]
Step 3: Find work done.
\[ W = q(V_B - V_C) = 0 \]
Step 1: Find distances from charge at $A$.
Since $ABC$ is an equilateral triangle: \[ AB = AC \]
Step 2: Compare potentials at $B$ and $C$.
\[ V_B = \frac{kQ}{AB}, \quad V_C = \frac{kQ}{AC} \] \[ AB = AC \Rightarrow V_B = V_C \]
Step 3: Find work done.
\[ W = q(V_B - V_C) = 0 \]
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