Electric Potential and Potential Energy
Potential is work done per unit charge in bringing a test charge from ∞, V = kQ/r, and U = qV for a charge placed in that potential.
What is Electric Potential and Potential Energy?
Potential is work done per unit charge in bringing a test charge from ∞, V = kQ/r, and U = qV for a charge placed in that potential.
Key formula / rule: V = kQ/r; potentials add as scalars.
Key points
- Compute potential and potential energy for charge configurations.
- Relate field and potential through E = -dV/dr.
Common exam trap
Adding potentials as vectors.
Definitions
- Term
Electric Potential and Potential Energy
- Meaning
Potential is work done per unit charge in bringing a test charge from ∞, V = kQ/r, and U = qV for a charge placed in that potential.
- Term
Electric Potential and Potential Energy — explanation
- Meaning
Potential is a scalar, so contributions add arithmetically, which makes it far easier to handle than the field for many-charge systems. Equipotential surfaces are always perpendicular to field lines.
Learning objectives
Compute potential and potential energy for charge configurations.
Relate field and potential through E = -dV/dr.
Formulae
- Key point
V = kQ/r; potentials add as scalars.
- Key point
E = -dV/dr; equipotentials are perpendicular to field lines.
- Key point
A conductor is an equipotential volume in electrostatic equilibrium.
Prerequisites
PHY-U5-ELS-T1-S1-C2
PHY-U1-WEP-T1-S2-C1
Common mistakes
Adding potentials as vectors.
Assuming zero potential implies zero field, or the reverse.
Keywords
Electric
Potential
Potential
Energy
Practice preview
What is the definition of electric potential at a point in an electric field?…
easy
Three point charges, +q, +q, and -q, are placed at the vertices of an equilateral triangle of side 'a'. What is the electric potential energy of this system? (Given: k = 1/(4πε₀))…
medium
A uniformly charged ring of radius R has a total charge Q. What is the electric potential at a point on its axis at a distance x from the center of the ring? (Given: k = 1/(4πε₀))…
hard