Overview
This lecture covers the fundamentals of electric fields, including forces between charges, electric field lines, field strength, potential, and applications such as uniform fields and equipotentials, aligned with the AQA Physics syllabus.
Forces Between Charges
- The force between two point charges in a vacuum is ( F = \frac{1}{4\pi\epsilon_0} \frac{|q_1 q_2|}{r^2} ).
- (\epsilon_0) (permittivity of free space) is approximately (8.85 \times 10^{-12}) and air can be treated as a vacuum.
- Charges of the same sign repel, opposite signs attract.
- For charged spheres, treat charge as concentrated at the center when measuring distance ( r ).
Example Problems: Electrostatic Force
- Halving the distance between charges increases force by a factor of four (( F \propto 1/r^2 )).
- Changing the magnitude of charges alters the force proportionally (( F \propto q_1q_2 )).
- Electric force can be compared to gravitational force; electrostatic forces are much stronger at subatomic scales.
Electric Field Lines & Representation
- Electric field: region where a positive test charge experiences a force.
- Field lines show the direction of force on a positive charge; out of positive, into negative.
- Field line density indicates field strength; lines leave or enter surfaces at 90°.
- Between two charges, field lines go from positive to negative.
Electric Field Strength
- Defined as the force per unit positive charge: ( E = F/q ).
- For radial (point) fields: ( E = \frac{Q}{4\pi\epsilon_0 r^2} ) (source charge ( Q ), distance ( r )).
- Units: N/C or V/m; base units: kg·m·s(^{-3})·A(^{-1}).
Uniform Electric Fields
- Between parallel plates: ( E = V/d ) (voltage ( V ), plate separation ( d )).
- Work done moving a charge: ( W = q\Delta V ).
- Acceleration in field: ( a = Eq/m = Vq/(dm) ).
- To balance weight: ( V = mgd/q ).
Motion of Charges in Fields
- Charged particles curve in uniform fields; trajectory depends on initial speed and field strength.
- Acceleration perpendicular to motion due to constant field.
- Example: Calculate if an electron escapes plates by comparing travel distance and time.
Electric Potential & Energy
- Electric potential (( V )): work done per unit charge bringing a charge from infinity.
- For radial fields: ( V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r} ).
- Potential difference: ( \Delta V = W/q ).
- Potential energy between two charges: ( U = \frac{q_1q_2}{4\pi\epsilon_0 r} ).
Equipotential Lines
- Equipotential lines: locations of constant potential, always perpendicular to field lines.
- No work done moving charge along an equipotential.
- Spacing increases as field strength decreases with distance.
- At equal potential, moving along the line changes neither electric potential energy nor speed.
Key Terms & Definitions
- Electric field — Region where a force acts on a charge.
- Permittivity ((\epsilon_0)) — Measure of medium's ability to permit electric field.
- Electric field strength ((E)) — Force per unit charge ((E = F/q)).
- Equipotential — Line or surface where potential is constant.
- Electric potential ((V)) — Work per unit charge to move from infinity to a point.
Action Items / Next Steps
- Practice solving problems using ( F = \frac{1}{4\pi\epsilon_0}\frac{|q_1q_2|}{r^2} ) and ( E = V/d ).
- Review worked examples of motion in electric fields and equipotential concepts.
- Next topic: Revise capacitors in the AQA syllabus.