Electro-Magnetic

D2 - Electric and Magnetic Fields (SL + HL)

Direction of Forces Between Two Types of Electric Charge
Opposite charges attract, like charges repel. The force acts along the line joining the charges.

Coulomb’s Law
F = k q1 q2 / r^2
where k = 1.4 × 10^11 (in appropriate units)
The magnitude of the force depends on the product of charges and inversely on the square of their distance.

Conservation of Electric Charge
Electric charge can neither be created nor destroyed, only transferred.

Millikan’s Oil Drop Experiment
Demonstrated that electric charge is quantized; charge exists in integer multiples of a fundamental unit (electron charge).

Transfer of Electric Charge: Friction, Induction, Contact, Grounding
Charges move by rubbing (friction), rearranging charges without touching (induction), touching (contact), or via earth ground (grounding).

Electric Field Strength
E = F / q
Defines force per unit positive charge placed in the field.

Electric Field Lines
Visual representation of field direction and strength: lines from positive to negative, denser lines indicate stronger field.

Field Line Density and Field Strength Relationship
More lines per area = stronger electric field.

Uniform Electric Field Between Parallel Plates
E = V / d
Field strength equals voltage divided by plate separation.

Motion of a Charged Particle in a Uniform Electric Field
Particle accelerates along field lines; equations of motion apply.

Electric Potential Energy (Ep)
Work done to assemble charged system from infinite separation.

Electric Potential at a Point
Ve = k * Q / r
Work done per unit charge bringing a test charge from infinity.

Electric Field as Potential Gradient
E = - dVe / dr
Field strength equals negative rate of change of potential with distance.

Work Done Moving Charge
W = q * Ve
Energy transferred moving charge in a potential.

Equipotential Surfaces
Surfaces where potential is constant; no work done moving charge along them.

Relation Between Equipotential Surfaces and Field Lines
Equipotentials are perpendicular to field lines.

B5 - Current and Circuits

Cells Provide emf (Electromotive Force)
Energy per unit charge supplied by a source.

Chemical Cells and Solar Cells as Energy Sources
Used to convert chemical or light energy into electrical energy.

Circuit Diagrams
Show the arrangement of components using standard symbols.

Direct Current (dc)
I = q / t
Current equals charge divided by time.

Potential Difference
V = W / q
Potential difference equals work done per unit charge.

Conductors vs. Insulators
Conductors have mobile charge carriers; insulators do not.

Origin of Electrical Resistance
Collisions between electrons and atoms impede electron flow.

Resistance
R = V / I
Resistance equals potential difference divided by current.

Resistivity
ρ = R * A / L
Resistivity equals resistance multiplied by cross-sectional area divided by length.

Ohm’s Law
V ∝ I (for ohmic conductors at constant temperature)
Voltage is directly proportional to current.

Ohmic vs. Non-Ohmic Behavior
Ohmic conductors follow Ohm’s law; non-ohmic materials (like filament lamps) do not, often due to heating effects.

Electrical Power Dissipated
P = I V = I^2 R = V^2 / R
Power can be expressed in three equivalent forms depending on known quantities.

Resistors in Series and Parallel
Series: Rs = R1 + R2 + ...
Parallel: 1/Rp = 1/R1 + 1/R2 + ...

Cells Characterized by emf and Internal Resistance
V = I * (R + r)
Terminal potential difference equals current times total resistance (external + internal).

Variable Resistors
Includes thermistors, LDRs, and potentiometers, where resistance changes with temperature, light intensity, or mechanical adjustment.

D3 - Motion in Electromagnetic Fields

Motion of Charged Particle in a Uniform Electric Field
(covered in D2)

Magnetic Field Lines
(covered in D2)

Motion of Charged Particle in a Uniform Magnetic Field
The magnetic force acts perpendicular to velocity, producing circular motion.

Motion of Charged Particle in Perpendicular Electric and Magnetic Fields
At certain velocities, electric and magnetic forces can balance, creating a velocity selector.

Force on a Charge Moving in a Magnetic Field
F = q v B

Force on a Current-Carrying Conductor in a Magnetic Field
F = B I L

Force per Unit Length Between Parallel Wires
F / L = (μ0 I1 I2) / (2π * r)

D4 - Induction (HL)

Magnetic Flux
Φ = B * A
Flux equals magnetic field strength times area.

Faraday’s Law (Induced emf)
E = -N * (ΔΦ / Δt)
Induced emf equals negative rate of change of magnetic flux multiplied by number of turns.

Induced emf in a Moving Conductor
E = B v L
Emf induced in a conductor moving perpendicularly through a magnetic field.

Lenz’s Law
The direction of induced emf opposes the change in magnetic flux that produced it.

Sinusoidal emf in Rotating Coil
A coil rotating in a uniform magnetic field produces a sinusoidal emf. The frequency of rotation affects both the amplitude and frequency of the induced emf.