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Physics 2 Unit 2: Electric force, field and potential

Charges exert forces described by Coulomb's law, create electric fields, and have electric potential energy and potential.

Covers: Electric charge and conservation, Coulomb's law, electric fields, electric potential energy, electric potential and potential difference, equipotential lines, capacitors

Study guide

Electric charge comes in two types, positive and negative; like charges repel and opposite charges attract. Charge is conserved and quantized in units of the elementary charge e = 1.6 × 10⁻¹⁹ C. Objects become charged by friction, conduction (contact) or induction (without contact). Conductors let charges move freely, and insulators don't. In a conductor at equilibrium, excess charge sits on the surface and the field inside is zero. Coulomb's law gives the force between point charges: F = k|q₁q₂|/r², where k = 9.0 × 10⁹ N·m²/C². The force follows an inverse-square law, so doubling the distance cuts the force to one-fourth.

An electric field E is the force per unit positive test charge: E = F/q. A point charge creates a field E = kq/r², pointing away from positive charges and toward negative ones. Field lines never cross, and their density shows field strength. Between parallel plates, the field is uniform: E = ΔV/d. A charge in a field feels F = qE; a positive charge accelerates along the field, and a negative charge accelerates opposite it.

Electric potential energy for two point charges is UE = kq₁q₂/r. Electric potential (voltage) is potential energy per unit charge: V = kq/r for a point charge, measured in volts (J/C). Potential is a scalar, so potentials from several charges add algebraically. Work done by the field relates to potential difference: W = −qΔV, and the change in potential energy is ΔUE = qΔV. Equipotential lines are perpendicular to field lines, and no work is done moving a charge along one. Positive charges move naturally from high to low potential. A capacitor stores charge and energy: C = Q/ΔV. For parallel plates, C = κε₀A/d, and the stored energy is UC = ½QΔV = ½C(ΔV)². Inserting a dielectric increases capacitance.

The electric potential energy of a group of charges is the sum of kq₁q₂/r over every pair. It equals the work an outside force must do to bring the charges together from infinitely far apart. Bringing like charges together takes positive work, and bringing opposite charges together takes negative work. In the uniform field between parallel plates, a charged particle feels a constant force qE. If it enters moving parallel to the plates, it follows a parabolic path like a projectile, with constant velocity along the plates and constant acceleration qE/m across them.

When conductors touch, charge flows until they reach the same electric potential. Outside a uniformly charged sphere, the field and potential are the same as if all the charge were a point at the center. The electric field always points toward lower potential.

Key ideas

• Like charges repel; opposite charges attract; charge is conserved.
• Coulomb's law is an inverse-square law.
• Electric field is force per unit charge.
• Potential is a scalar; equipotentials are perpendicular to field lines.
• Capacitors store charge and energy: C = Q/ΔV.

Formulas and rules

Common mistakes

• Adding electric potentials as vectors; potential is a scalar.
• Forgetting that doubling distance quarters the Coulomb force.

Words to know

Electric charge

A property of matter that causes electric forces.

Elementary charge

The charge of a proton, 1.6 × 10⁻¹⁹ C.

Conservation of charge

Total charge in an isolated system stays constant.

Conductor

A material that lets charges move freely.

Insulator

A material that doesn't let charges move freely.

Induction

Charging an object without contact.

Coulomb's law

F = k|q₁q₂|/r².

Electric field

Force per unit positive charge.

Field lines

Lines showing the direction of the electric field.

Uniform field

A field with constant magnitude and direction.

Electric potential energy

Energy due to the positions of charges.

Electric potential

Potential energy per unit charge, in volts.

Potential difference

The change in electric potential between two points.

Equipotential line

A line of constant electric potential.

Capacitor

A device that stores charge and energy.

Capacitance

The charge stored per volt: C = Q/ΔV.

Dielectric

An insulator that increases capacitance.

Sample practice questions

11 more questions like these, from level 1 to 5, are in the practice set.