Two identical point charges +3.62x10-6C are placed at two neighbouring corners of a square. The length of each side of the square is 10.4m. Find the electric potential at an empty corner of the square (not occupied by the point charges) in kV. The Coulomb’s law constant=k=8.99x109Nm2/C2. Assume the potential at an infinite distance from the charges is zero.

Question

Two identical point charges +3.62x10-6C are placed at two neighbouring corners of a square. The length of each side of the square is 10.4m.  Find the electric potential at an empty corner of the square  (not occupied by the point charges) in kV. The Coulomb’s law constant=k=8.99x109Nm2/C2. Assume the potential at an infinite distance from the charges is zero.

BlackTom AI · Accepted Answer

Examining the problem, the key task is to compute the electric potential at the empty corner due to the two charges located at the adjacent corners of the square.
First, identify the geometry: a square with side length a = 10.4 m, and two identical point charges q = 3.62 x 10^-6 C placed at neighboring corners, say at A and B. The empty corner to evaluate the potential at is the corner C that is diagonally opposite A and adjacent to B.
Next, determine the distances from the two charges to the evaluation point at C:
- Distance from A to C is the diagonal of the square: r1 = a * sqrt(2).
- Distance from B to C is along a side: r2 = a.
The electric potential at a point due to a single point charge is V = k*q/r. Since electric potential is a scalar, the potentials due to both charges simply add: V_total = k*q/r1 + k*q/r2 = k*q*(1/r1 + 1/r2).
Substitute the known values: r1 = a*sqrt(2) and r2 = a, so 1/r1 = 1/(a*sqrt(2)) and 1/r2 = 1/a. Therefore, V_total = k*q*(1/(a*sqrt(2)) + 1/a).
Compute step by step:
- Compute k*q: k*q = (8.99 x 10^9 N·m^2/C^2) * (3.62 x 10^-6 C) ≈ 3.2566 x 10^4 V·m.
- Compute the sum of the reciprocals: 1/a = 1/10.4 ≈ 0.0961538 m^-1; 1/(a*sqrt(2)) ≈ 0.0961538 / 1.4142136 ≈ 0.067999 m^-1; sum ≈ 0.1641528 m^-1.
- Multiply: V_total ≈ (3.2566 x 10^4) * 0.1641528 ≈ 5.35 x 10^3 volts.
Since the problem asks for the potential in kilovolts, V_total ≈ 5.35 kV, which aligns with the given numerical result around 5.34 kV. 
Note: Potential adds linearly for multiple point charges, so no cross terms or interactions between the charges alter this simple superposition at the specified point. The distances used are purely geometric, derived from the square’s side length and the relative positions of the charges and the evaluation point.

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