The direction of a field line at a point in space represents

The direction of a field line at a point in space represents

• A. The direction of the force on a positive test charge placed at that point
• B. The direction of potential energy change
• C. The direction of motion of a free charge at that point
• D. The gradient of the charge density

Answer: (A)

Electric field lines indicate the direction of the electric field vector at that point, which is the force per unit positive test charge. Since F = qE, a small positive test charge placed there experiences a force in the same direction as the field, so the tangent to the field line shows the direction of the force on a positive test charge. The other ideas don’t match because the direction of potential energy change follows the gradient of the potential (the force relates to the negative gradient of potential energy, not the field-line direction), motion of a free charge depends on its velocity and other conditions rather than just the field lines, and the gradient of charge density isn’t what field lines depict.

Electric field lines indicate the direction of the electric field vector at that point, which is the force per unit positive test charge. Since F = qE, a small positive test charge placed there experiences a force in the same direction as the field, so the tangent to the field line shows the direction of the force on a positive test charge. The other ideas don’t match because the direction of potential energy change follows the gradient of the potential (the force relates to the negative gradient of potential energy, not the field-line direction), motion of a free charge depends on its velocity and other conditions rather than just the field lines, and the gradient of charge density isn’t what field lines depict.