Topic 6: Electric and Magnetic Fields

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6A: Electric Fields

An electric field is a region where a charged particle experiences a force. We model these using field lines that point from positive to negative.

1. Coulomb’s Law

The force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

$$F=\frac{Q_1{Q}_2}{4\pi {\epsilon }_0{r}^2}$$

2. Electric Field Strength (E)

Defined as the force per unit positive charge.

• Radial Fields: $E=\frac{Q}{4\pi {\epsilon }_0{r}^2}$
• Uniform Fields: $E=\frac{V}{d}$

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6B: Capacitors

Capacitors are devices that store charge and, consequently, electrical energy.

1. Capacitance (C)

The charge stored per unit potential difference across the plates. Unit: Farad (F).

$$C=\frac{Q}{V}$$

2. Energy Stored

The work done to charge a capacitor is stored as electric potential energy. This is the area under a Q-V graph.

$$W=\frac{1}{2}QV=\frac{1}{2}C{V}^2$$

3. Charging and Discharging

The rate of charge flow depends on the Time Constant (τ = RC).

[Image of capacitor charging and discharging graphs]

Process	Equation (Potential Difference)
Discharging	$V=V_0{e}^{\frac{-t}{RC}}$
Charging	$V=V_0(1-e^{\frac{-t}{RC}})$

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6C: Electromagnetic Effects

1. Magnetic Force on a Moving Charge

A charge q moving with velocity v through a magnetic field B experiences a force:

$$F=Bqv\sin \left(\theta \right)$$

Use Fleming's Left Hand Rule to find the direction of force for a positive charge.

[Image of Fleming's Left Hand Rule]

2. Magnetic Flux (Φ) and Flux Linkage (NΦ)

• Magnetic Flux: $\Phi =BA$ (Unit: Weber, Wb)
• Flux Linkage: $N\Phi =BAN$

3. Faraday’s and Lenz’s Law

Faraday's Law: The magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage.

Lenz's Law: The direction of the induced e.m.f. is such that it opposes the change that created it (Conservation of Energy).

$$\epsilon =-N\frac{d\Phi }{dt}$$