Electric Potential

Why it matters

Electric potential is a fundamental concept in electrical engineering that helps us understand how energy is stored and transferred in electric fields and circuits. It is essential for designing and analyzing electrical systems, from simple circuits to complex power grids.

Key ideas

• Electric Potential (V): The work done in bringing a unit positive charge from infinity to a point in an electric field without acceleration. It is a scalar quantity.
• Potential Difference (Voltage): The difference in electric potential between two points. It is what drives current in a circuit.
• Equipotential Surfaces: Surfaces where the electric potential is the same everywhere. No work is done when moving a charge along an equipotential surface.
• Relation to Electric Field (E): The electric field is the negative gradient of the electric potential. This means that the electric field points in the direction of the greatest decrease of potential.

These relations refer to electrostatics. Potential is relative to a chosen reference; infinity is convenient only where that reference is finite. W below is quasistatic external work, so ΔV = W_ext/q = −W_field/q. In general E = −∇V; −dV/dr is the radial component for V(r).

Formulas

• V = W / Q
  • V: Electric potential (Volts, V)
  • W: Work done (Joules, J)
  • Q: Charge (Coulombs, C)
• E = -dV / dr
  • E: Electric field intensity (Volts per meter, V/m)
  • dV: Change in electric potential (Volts, V)
  • dr: Change in position (meters, m)

Worked example

Given: A point charge of 5 μC is located at the origin in vacuum, with V = 0 at infinity. Calculate the electric potential at a point 3 meters away from the charge.

1. Identify the formula: V = k * Q / r where k is Coulomb's constant (8.99 x 10^9 N·m²/C²), Q is the charge, and r is the distance from the charge.
2. Substitute the values: V = (8.99 x 10^9 N·m²/C²) * (5 x 10^-6 C) / 3 m
3. Calculate: V = 14,983.33 V

Final Answer: 14,983.33 V

Common mistakes

• Confusing electric potential with electric potential energy.
• Forgetting that electric potential is a scalar quantity, not a vector.
• Not considering the sign of the charge when calculating potential.

For GATE EE

Questions often involve calculating the electric potential at a point due to one or more charges, understanding equipotential surfaces, and relating electric potential to electric field intensity. Practice problems involving both point charges and continuous charge distributions.

Quick check

1. What is the unit of electric potential?
2. How is electric field related to electric potential?
3. What happens to the potential energy of a charge when it moves along an equipotential surface?

Answers: 1. Volt (V), 2. E = -dV/dr, 3. It remains constant.