Consider the following statements regarding Electric Potential:1.Electric potential is defined as work done in bringing a unit positive charge from infinity to a point.2.Potential difference between two points is independent of the path taken between them.3.Electric potential is a vector quantity since it has magnitude and direction.4.Equipotential surfaces are always perpendicular to electric field lines.Which of the above statements is/are correct?

Correct Answer: D - 1, 2 and 4 only

Quick Concept Explanation

The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles. Key relation: E=−∇V; ΔV=−∫E·dl.

Exam focus: Potential is scalar; electric field is vector. Common trap: Do not assign a direction to electric potential.

Statement-wise Verification

• Statement 1 - Correct.
  Electric potential is defined as work done in bringing a unit positive charge from infinity to a point.
  Potential is scalar; electric field is vector.
• Statement 2 - Correct.
  Potential difference between two points is independent of the path taken between them.
  The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential.
• Statement 3 - Incorrect.
  Electric potential is a vector quantity since it has magnitude and direction.
  The correct principle is: Potential is scalar; electric field is vector.
• Statement 4 - Correct.
  Equipotential surfaces are always perpendicular to electric field lines.
  Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles.

Core Concept

Electrostatic potential is a scalar. The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles.

Formula / Key Relationship

E=−∇V; ΔV=−∫E·dl.

Why the Other Options Are Wrong

Option A is incorrect because it includes incorrect statement(s) 3. Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option C is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1, 4.

Exam Shortcut / Approach

Potential is scalar; electric field is vector.

Common Mistake

Do not assign a direction to electric potential.

Quick Revision

Potential and Equipotential Surfaces is linked with Electric Potential, Electrostatics and Electromagnetic Fields. Potential is scalar; electric field is vector.