18. Electric fields

An electric field is a region in which a charge experiences a force; field strength E is force per unit positive charge.

Use a small positive test charge to define direction, then calculate force on any charge with its sign included.

Between parallel charged plates, a positive charge feels force in the field direction and a negative charge opposite it.

The field exists without placing a test charge, and field direction is not always the same as force on a negative charge.

Electric field strength satisfies E=F/q, so the force on charge q is F=qE; direction reverses for negative q.

Use E as a vector and q with sign. In a uniform field, force and acceleration are constant if q and mass are constant.

A −2 μC charge in a 3.0×10⁴ N C⁻¹ field experiences 0.060 N opposite the field direction.

E is not force itself and does not depend on the test charge used to measure it.

Electric field lines point in the direction of force on a positive test charge; closer lines indicate stronger field qualitatively.

Lines start on positive charge and end on negative charge or infinity, do not cross, and are perpendicular to conductor surfaces in electrostatic equilibrium.

Parallel equally spaced lines represent a uniform field between large oppositely charged plates.

A negative charge moves opposite to the arrow direction, and field-line density is a model rather than an exact numerical scale.

In a uniform field, field strength magnitude is E=∆V/∆d, where ∆V is potential difference across perpendicular separation ∆d.

Use metres and volts, and remember field direction points from higher potential toward lower potential for a positive test charge.

A 600 V difference across 0.020 m gives E=3.0×10⁴ N C⁻¹.

The relation is for a uniform field; in a point-charge field strength changes with distance.

A charge in a uniform field feels F=qE, so if q and mass are constant its acceleration is constant and directed with or against E according to charge sign.

Resolve initial velocity into components: the field changes the component along its force while perpendicular motion remains uniform in the ideal model.

An electron entering a uniform vertical field follows a curved path because horizontal velocity persists while vertical acceleration acts.

A negative charge accelerates opposite the field direction; the field does not automatically stop all motion.

For a spherical conductor in electrostatic equilibrium, excess charge resides on the surface and the external field acts as if total charge Q were at the centre.

Use centre distance r and remember the field inside the conductor is zero in electrostatic equilibrium.

A charged metal sphere produces an external field decreasing as 1/r², even though the charge is spread over its surface.

The point-charge equivalence does not describe the field inside the conductor or an irregular charged object without symmetry.

Two point charges exert forces of magnitude F=|Q₁Q₂|/(4πε₀r²), along their joining line; like charges repel and unlike charges attract.

Use centre separation r and treat the force as a vector when multiple charges act. Include signs to determine direction.

Doubling one charge doubles force, while doubling separation quarters it.

The inverse-square separation is not the distance from a charge’s surface, and equal force magnitudes act on both charges.

The field magnitude due to point charge Q at distance r is E=|Q|/(4πε₀r²), directed away from positive Q and toward negative Q.

The field is a property of the source, independent of the test charge used to measure it. Add fields as vectors for several sources.

At twice the distance from a point charge, field strength is one quarter as large.

E is not the force on every charge; the force is qE and depends on the test charge.

Electric potential V at a point is work done per unit positive test charge bringing it from infinity, with zero potential at infinity.

Potential is scalar, so contributions add algebraically; electric field is a vector and requires direction.

A positive point charge gives positive potential, while a negative source gives negative potential relative to infinity.

Potential is not force per charge—that is field strength—and equal potential does not mean zero field everywhere.

Electric field strength points in the direction of decreasing electric potential; in one dimension E=−dV/dr.

The minus sign links field direction to potential fall. In a uniform field, the gradient is constant; near a point charge it changes with distance.

A potential drop of 20 V over 0.010 m in the field direction corresponds to E≈2000 N C⁻¹.

Electric field is not potential itself; a high potential region can have zero field if potential is locally constant.

For a point charge Q with zero potential at infinity, V=Q/(4πε₀r), with sign set by Q.

Potential is scalar, so potentials from several charges add algebraically. Use centre distance r and distinguish V from field strength.

Doubling distance from a positive point charge halves its positive potential.

Potential does not follow the inverse-square law—that applies to field magnitude, while point-charge potential follows 1/r.

A charge q at electric potential V has electric potential energy E_P=qV relative to the chosen zero; changes satisfy ∆E_P=q∆V.

Include the charge sign and reference level. A positive charge moving to lower V loses potential energy; a negative charge reverses that trend.

Moving a +2 μC charge through a 50 V rise increases potential energy by 1.0×10⁻⁴ J.

Potential is a property of the field location, whereas potential energy depends on both location and charge.