Electric Potential Difference and Work

Electric Potential Difference and Work

Potential difference tells how much electrical energy changes for every coulomb that moves between two places.

Like moving downhill gravitationally, a positive charge naturally tends to move toward lower electric potential when only the electric force acts.

Electric Potential Difference and Work

Definition

Potential difference between two points is the change in electric potential energy per unit charge when a charge moves between those points.

Meaning of Potential Difference

Between points `A` and `B`:

**ΔV = V_B − V_A**

Potential-energy change:

**ΔU = qΔV**

Therefore:

**ΔV = ΔUq**

For work done by the electric field:

**W_field = −ΔU**

so:

**W_field = q(V_A−V_B)**

For an external agent moving the charge slowly with no change in kinetic energy:

**W_external = ΔU = q(V_B−V_A)**

A potential difference of `1 V` means that the electric potential energy changes by `1 J` for every `1 C` of charge.

Electric Field Relation

For a uniform electric field and displacement `d` parallel to the field:

**ΔV = −Ed**

The negative sign shows that electric potential decreases in the direction of the electric field.

Formula / Key Relation

**ΔV=ΔUq**

**ΔU=qΔV**

**W_field=−qΔV**

Uniform field:

**ΔV=−Ed**

when displacement is along the field.

Electric Potential Difference and Work — Advanced

For electrostatics:

**V_B−V_A = −∫A→B E·dl**

Thus potential differences are line integrals of the conservative electric field.