Which expression best represents the superposition of fields from two charges at a point?

Which expression best represents the superposition of fields from two charges at a point?

• A. E = E1 + E2; E_i = k q_i (r − r_i)/|r − r_i|^3
• B. E = E1 × E2; E_i = k q_i (r − r_i)/|r − r_i|^3
• C. E = E1 − E2; E_i = k q_i (r − r_i)/|r − r_i|^3
• D. E = E1 / E2; E_i = k q_i (r − r_i)/|r − r_i|^3

Answer: (A)

Superposition means fields from different charges add vectorially at each point in space. For a single point charge at position r_i, the field is E_i(r) = k q_i (r − r_i) / |r − r_i|^3. With two charges, the total field is the sum of the two contributions: E(r) = E1(r) + E2(r) = k q1 (r − r1)/|r − r1|^3 + k q2 (r − r2)/|r − r2|^3. This is the expression that reflects the additive, vector nature of electrostatic fields. The other operations (multiplication, subtraction, division) would not describe how fields from separate sources combine.

Superposition means fields from different charges add vectorially at each point in space. For a single point charge at position r_i, the field is E_i(r) = k q_i (r − r_i) / |r − r_i|^3. With two charges, the total field is the sum of the two contributions: E(r) = E1(r) + E2(r) = k q1 (r − r1)/|r − r1|^3 + k q2 (r − r2)/|r − r2|^3. This is the expression that reflects the additive, vector nature of electrostatic fields. The other operations (multiplication, subtraction, division) would not describe how fields from separate sources combine.