The electric field E at a point is defined as the force on a test charge divided by the test charge. Which statement correctly expresses this relation?

The electric field E at a point is defined as the force on a test charge divided by the test charge. Which statement correctly expresses this relation?

• A. E = F/q0
• B. E = F/q0 in the direction of F
• C. E = k q / r^2 r̂
• D. E = q0 / (4 π ε0 r^2)

Answer: (B)

Electric field is the force per unit positive test charge, so it is a vector defined by E = F/q0. Since F is a vector, dividing by the scalar q0 gives a vector in the same direction as the force on a positive test charge. This means the field points in the direction you would push a positively charged test charge. The magnitude of E is the force divided by the test charge, and the direction aligns with F for a positive q0. The other forms describe specific point-charge fields or would misstate the dependence on the test charge, so they don’t capture the general definition.

Electric field is the force per unit positive test charge, so it is a vector defined by E = F/q0. Since F is a vector, dividing by the scalar q0 gives a vector in the same direction as the force on a positive test charge. This means the field points in the direction you would push a positively charged test charge. The magnitude of E is the force divided by the test charge, and the direction aligns with F for a positive q0. The other forms describe specific point-charge fields or would misstate the dependence on the test charge, so they don’t capture the general definition.