Electric Potential: Core Concepts and Applications

Electric Potential: Definition and Fundamentals

Electric potential at a point is the work required to move a unit positive charge from infinity to that point within an electric field. It is defined by the formula: V_A = KQ / r_A

The unit of electric potential is the volt (V), defined as Joules per Coulomb (J/C). A point has a potential of one volt when one Joule of work is required to move a charge of one Coulomb from infinity to that point.

Key Properties of Electric Potential

• Electric potential can be positive or negative, depending on the sign of the charge (Q) that creates the field. A positive charge creates a positive potential, while a negative charge creates a negative potential.
• All points equidistant from a point charge that creates the field form a spherical equipotential surface.

Electric field lines are always perpendicular to equipotential surfaces.

Electric Potential from Multiple Point Charges

The electric potential at a point due to a system of two or more point charges is obtained by applying the principle of superposition. This means the total potential at a point in the field is the algebraic sum of the potentials due to each individual point charge.

V = V₁ + V₂ + ... + V_n = K ∑ (Q_i / r_i), where r_i is the distance from charge Q_i to the point where the potential is being calculated.

Electric Potential Difference Between Two Points

The electric potential difference (ΔV) between two points is defined as the work done by the electric field to move a unit positive charge from one point to another.

The potential difference between points A and B is given by: V_B - V_A = W_AB / q. Alternatively, applying the definition of potential at each point, we get: V_B - V_A = (KQ / r_B) - (KQ / r_A) = KQ (1 / r_B - 1 / r_A).

Similar to the gravitational field, the zero of electric potential is typically defined at an appropriate reference point, usually at infinity.

Electric Potential and Field Intensity Relationship

By comparing the expressions for electric field intensity (|E|) and electric potential (V) at a point, we have: V = KQ / r and |E| = KQ / r². From these, we can see that V = |E|r. In general, electric field strength and potential are related by the expression: dV = -E ⋅ dr. This relationship allows the electric field to be expressed in Volts per meter (V/m), where 1 N/C = 1 V/m. The expression -dV/dr (or -∇V in 3D) is called the potential gradient, which gives the electric field.

Electric Field Potential Variation with Distance

In a uniform electric field, the potential difference varies linearly with distance, decreasing in the direction of the field. The potential difference between two points A and B is given by: V_B - V_A = Ed, where E is the uniform field strength and d is the distance between A and B along the field direction. The variation of the potential energy (U) of a charge q when it moves from A to B is: U_B - U_A = q(V_B - V_A) = qEd.