What is the electric field produced by a single point charge q at distance r?

What is the electric field produced by a single point charge q at distance r?

• A. E = (1/(4π ε0)) (q / r) r_hat
• B. E = (1/(4π ε0)) (q / r^2) r_hat_12
• C. E = (1/(4π ε0)) (q / r^2) r_hat
• D. E = (1/(4π ε0)) (q r_hat / r^3)

Answer: (C)

The main idea is that the electric field from a point charge is radial and falls off with the square of the distance. The field points along the line from the charge to the observation point, described by the unit vector r̂, and its magnitude is k q / r^2, where k = 1/(4πε0). So the field at distance r is E = (1/(4πε0)) (q / r^2) r̂. This captures both the correct directional sense (away from the charge for positive q, toward it for negative q) and the correct distance dependence (1/r^2). The other forms don’t match this combination: one has the wrong power of r, another uses an unclear or incorrect direction vector, and another places r̂ in the numerator with r^3 in the denominator, which gives the wrong units and behavior.

The main idea is that the electric field from a point charge is radial and falls off with the square of the distance. The field points along the line from the charge to the observation point, described by the unit vector r̂, and its magnitude is k q / r^2, where k = 1/(4πε0).

So the field at distance r is E = (1/(4πε0)) (q / r^2) r̂. This captures both the correct directional sense (away from the charge for positive q, toward it for negative q) and the correct distance dependence (1/r^2).

The other forms don’t match this combination: one has the wrong power of r, another uses an unclear or incorrect direction vector, and another places r̂ in the numerator with r^3 in the denominator, which gives the wrong units and behavior.