How is the total electric potential at a point due to multiple point charges computed?

How is the total electric potential at a point due to multiple point charges computed?

• A. V = ∑ qi / ri
• B. V = ∑ qi / (k ri)
• C. V = ∑ k qi / ri
• D. V = ∑ qi / ri^2

Answer: (C)

The main idea is that electric potential adds up from each point charge (it’s a scalar quantity, so you simply sum them). For a single point charge q at a distance r, the potential is V = k q / r, where k = 1/(4πε0) ≈ 8.99×10^9 N m^2/C^2. For multiple charges, the total potential at a given point is the sum of the contributions from all charges: V_total = Σ k q_i / r_i, with r_i being the distance from the i-th charge to the point. This form is correct because you always include the constant k and you divide by the distance to that charge; omitting k (as in the first option) or placing k in the denominator (as in the second) gives the wrong magnitude, and using r_i^2 (as in the fourth option) would describe the electric field, not the potential.

The main idea is that electric potential adds up from each point charge (it’s a scalar quantity, so you simply sum them). For a single point charge q at a distance r, the potential is V = k q / r, where k = 1/(4πε0) ≈ 8.99×10^9 N m^2/C^2. For multiple charges, the total potential at a given point is the sum of the contributions from all charges: V_total = Σ k q_i / r_i, with r_i being the distance from the i-th charge to the point.

This form is correct because you always include the constant k and you divide by the distance to that charge; omitting k (as in the first option) or placing k in the denominator (as in the second) gives the wrong magnitude, and using r_i^2 (as in the fourth option) would describe the electric field, not the potential.