Question

Place several E-Field Sensors at a few points on different equipotential lines, and look at the relationship between the electric field and the equipotential lines. Which statement is true?
1-At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of higher voltages.
2-At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages.

3-At any point, the electric field is parallel to the equipotential line at that point.

Answer 1

Answer:

2.

Explanation:

• If a charge is moved along a equipotential line, no work is done on the charge.
• If we remember that the work done by an external force, is just the product of the component of the force parallel to the displacement, if the force produces no work, this means that is perpendicular to the displacement.
• So, as the electric field is just the force per unit charge, and has the same direction as the force (for a positive charge), it must be perpendicular to any equipotential line.
• As the electric field (by convention) has the same direction as it would be taken by a positive test charge, and positive charges move from higher voltages to lower ones, the electric field is directed toward lines of lower voltages (like it happens between the plates of a capacitor).