Introduction to Electric Potential

Electric Potential (V) at a point in an electric field is defined as the work done per unit positive charge in bringing a small test charge from infinity to that point, without acceleration.

V = \[\frac {W}{q}\]

• SI Unit: volt (V), where 1 V = 1 J/C
• Dimensional Formula: [M¹L²T⁻³A⁻¹]
• Nature: Scalar quantity (no direction, only magnitude)

V = \[\frac{1}{4\pi\varepsilon_0}\frac{qr}{R^3}=\frac{\rho r}{3\varepsilon_0}\]

where k = 9 × 10⁹ N m²/C², q is the source charge, and r is the distance from the charge.

Electric field is a vector quantity, which makes calculations involving direction cumbersome. Electric potential provides a scalar alternative that simplifies analysis of:

• Energy required to move a charge between two points
• The natural direction of charge movement
• Work done by or against the electric field

• A positive charge moves naturally from higher potential → lower potential (along the field direction).
• A negative charge moves naturally from lower potential → higher potential (opposite to the field direction).