# Electric and Magnetic Fields

> Physics · Edexcel IAL 2018
> Source: https://www.owlsprep.com/study/edexcel-ial-physics-u4-electric-and-magnetic-fields/

This guide covers all Edexcel IAL Physics Unit 4 content for electric fields, capacitance, RC circuits, magnetic forces, and electromagnetic induction, aligned with the 2018 WPH14 specification.

**Prerequisites:** Fluency with algebra, graph interpretation, and base-e logarithms; [Familiarity with SI units for electricity and magnetism](https://www.owlsprep.com/study/edexcel-ial-physics-u2-electricity/)

## Learning objectives

- Calculate electric field strength, force, and potential for radial and uniform electric fields
- Solve capacitance and energy storage problems using V-Q graph area and derived energy formulae
- Interpret RC charge/discharge curves and apply exponential/logarithmic RC equations to calculate time constant
- Calculate magnetic force on moving charges and current-carrying conductors using Fleming's Left Hand Rule
- Apply Faraday's and Lenz's laws to calculate induced emf magnitude and direction
- Carry out Core Practical 11 for capacitor charge/discharge to determine time constant experimentally

## Electric Fields (Radial and Uniform)

**Electric field strength** — Force per unit positive test charge in a field, given by $E = F/Q$

*Notation:* E

*Example:* A 2 nC charge experiences a force of 5×10⁻⁴ N in a field, so E = 2.5×10⁵ N C⁻¹

For **point charge radial fields**, use Coulomb's law to find force between two charges, and the derived radial field strength formula. For **uniform parallel plate fields**, field strength is constant and given by $E = V/d$, where V is potential difference between plates and d is separation.

$$F = \frac{Q_1 Q_2}{4\pi\varepsilon_0 r^2} \quad \text{(Coulomb's law)}$$

$$E = \frac{Q}{4\pi\varepsilon_0 r^2} \quad \text{(Radial electric field strength)}$$

$$V = \frac{Q}{4\pi\varepsilon_0 r} \quad \text{(Radial electric potential)}$$

**Worked example:** Calculate the electric field strength 0.2 m from a point charge of 3 μC. Use $1/4\pi\varepsilon_0 = 8.99 \times 10^9$ N m² C⁻².

1. Substitute values into the radial field formula:
2. $$E = \frac{Q}{4\pi\varepsilon_0 r^2} = \frac{8.99 \times 10^9 \times 3 \times 10^{-6}}{(0.2)^2}$$
3. Calculate the result: $E = 6.74 \times 10^5$ N C⁻¹, directed away from the positive point charge.

> **Field and equipotential rules**
>
> Field lines are always perpendicular to equipotential surfaces. Uniform fields have parallel, evenly spaced field lines and parallel flat equipotentials. Radial fields have field lines pointing to/from the point charge, and spherical equipotentials.

## Capacitance and Energy Storage

**Capacitance** — Charge stored per unit potential difference across a capacitor, $C = Q/V$, measured in farads (F)

*Notation:* C

*Example:* A capacitor storing 4 mC of charge at 12 V has capacitance 333 μF

Energy stored in a capacitor is equal to the area under the V-Q graph, leading to the base formula $W = \frac{1}{2}QV$. Two derived forms are given on the formula sheet for use when Q or V is unknown.

$$W = \frac{1}{2}CV^2 = \frac{Q^2}{2C}$$

**Worked example:** A 220 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored in the capacitor.

1. Use the $W = \frac{1}{2}CV^2$ formula, as we know C and V:
2. $$W = 0.5 \times 220 \times 10^{-6} \times (15)^2$$
3. Calculate the result: $W = 0.0248$ J, or 24.8 mJ.

## RC Circuit Charge and Discharge

**Time constant** — Time for charge/voltage/current in a discharging RC circuit to fall to 1/e (~37%) of its initial value, equal to $\tau = RC$

*Notation:* \tau

For discharging circuits, charge, current and voltage follow a decaying exponential curve. For charging circuits, they follow a rising exponential curve. The log-linear form of the discharge equation can be plotted to get a straight line with gradient $-1/RC$, used to find time constant experimentally (Core Practical 11).

$$Q = Q_0 e^{-t/RC} \quad \text{(Discharge charge equation)}$$

$$\ln Q = \ln Q_0 - \frac{t}{RC} \quad \text{(Log-linear discharge form)}$$

**Worked example:** A 470 μF capacitor discharges through a 10 kΩ resistor. Calculate the time taken for the charge to fall to 20% of its initial value.

1. First calculate the time constant: $\tau = RC = 10 \times 10^3 \times 470 \times 10^{-6} = 4.7$ s
2. Rearrange the log equation to solve for t when $Q/Q_0 = 0.2$:
3. $$t = RC \ln \left(\frac{Q_0}{Q}\right) = 4.7 \times \ln(5)$$
4. Calculate the result: $t = 7.56$ s

> **exam_tip**
>
> In Core Practical 11, you will measure voltage across the capacitor at regular time intervals during discharge, plot a ln(V) vs t graph, and find the gradient to calculate RC. The most common error is using base-10 logs instead of base-e logs for the plot.

## Magnetic Fields and Forces

**Magnetic flux density** — Force per unit current per unit length of conductor perpendicular to the magnetic field, measured in tesla (T)

*Notation:* B

*Example:* A 0.5 m wire carrying 2 A perpendicular to a 0.4 T field experiences force 0.4 N

Force on a current-carrying conductor is given by $F = BIl \sin\theta$, where θ is the angle between the current and magnetic field. Force on a moving charged particle is $F = Bqv \sin\theta$, where θ is the angle between velocity and B field. Use Fleming's Left Hand Rule to find force direction: first finger = B field, second finger = conventional current/positive charge velocity, thumb = force direction.

**Worked example:** An electron travels at $2 \times 10^6$ m s⁻¹ perpendicular to a 0.3 T magnetic field. Calculate the magnetic force on the electron. Charge of electron = $1.6 \times 10^{-19}$ C.

1. Since θ = 90°, $\sin\theta = 1$. Substitute values into the force formula:
2. $$F = Bqv = 0.3 \times 1.6 \times 10^{-19} \times 2 \times 10^6$$
3. Calculate the result: $F = 9.6 \times 10^{-14}$ N. Use Fleming's Left Hand Rule, reversing the current direction for the negative electron, to find force direction.

> **Fleming's Left Hand Rule memory aid**
>
> **F**irst finger = **F**ield, se**C**ond finger = **C**urrent, Th**u**mb = Th**r**ust (force). All three fingers are held perpendicular to each other.

## Electromagnetic Induction

Induced emf is generated when there is a change in flux linkage through a coil, either by relative motion between a magnet and coil, or change in current in a linked coil. Faraday's law gives the magnitude of induced emf, while the negative sign in the formula encodes Lenz's law, which states induced emf opposes the change that caused it.

> **warning**
>
> You do not need to differentiate the flux linkage equation. Use $|E| = N\Delta\phi/\Delta t$ for average emf, or find the gradient of a flux linkage-time graph for instantaneous emf.

**Worked example:** A 50-turn coil with area 0.02 m² is placed perpendicular to a 0.8 T magnetic field. The field is reduced to 0 T in 0.1 s. Calculate the average induced emf.

1. Calculate change in flux linkage: $\Delta(N\phi) = N \times \Delta B \times A = 50 \times 0.8 \times 0.02 = 0.8$ Wb turns
2. Apply Faraday's law for average emf:
3. $$|E| = \frac{\Delta(N\phi)}{\Delta t} = \frac{0.8}{0.1} = 8 \text{ V}$$

## Common pitfalls

- **Wrong:** Using $E = V/d$ for radial electric fields
  - Why it fails: $E = V/d$ only applies to uniform parallel plate fields; radial fields follow the inverse square law.
  - Correct: Use $E = Q/(4\pi\varepsilon_0 r^2)$ for point charge radial fields, reserve $E = V/d$ exclusively for uniform fields.
- **Wrong:** Forgetting the $\sin\theta$ term in magnetic force calculations
  - Why it fails: Force is zero when current/velocity is parallel to the B field, maximum only when perpendicular.
  - Correct: Always use θ = angle between current/velocity direction and magnetic field lines, even if θ = 90° (sinθ = 1) to avoid errors.
- **Wrong:** Using the decaying exponential $Q = Q_0 e^{-t/RC}$ for charging RC circuits
  - Why it fails: The decaying form applies only to discharge; charging follows a rising exponential $Q = Q_0(1 - e^{-t/RC})$.
  - Correct: Match the exponential form to the process: falling curves = discharge, rising curves = charging.
- **Wrong:** Calculating capacitor energy as $W = QV$ instead of $W = \frac{1}{2}QV$
  - Why it fails: Energy stored is the area under the V-Q graph, not the product of final charge and voltage values.
  - Correct: Use only the three given energy formulae: $\frac{1}{2}QV$, $\frac{1}{2}CV^2$, or $\frac{Q^2}{2C}$.
- **Wrong:** Ignoring the negative sign in Faraday's law as irrelevant
  - Why it fails: The negative sign encodes Lenz's law, which requires you to state that induced emf opposes the change in flux linkage.
  - Correct: Use the magnitude for calculation, but explicitly reference Lenz's law to explain emf direction when asked.

## Cheatsheet

| Formula | Context | Units | Key Note |
| --- | --- | --- | --- |
| $E = F/Q$ | All electric fields | N C⁻¹ / V m⁻¹ | Definition of electric field strength |
| $F = Q_1Q_2/4\pi\varepsilon_0r^2$ | Force between two point charges | N | Repulsive for like charges, attractive for opposite |
| $E = V/d$ | Uniform parallel plate fields | N C⁻¹ | Only valid for constant field between plates |
| $C = Q/V$ | Capacitance definition | F | 1 F = 1 C V⁻¹ |
| $W = \frac{1}{2}QV$ | Capacitor stored energy | J | Equal to area under V-Q graph |
| $\tau = RC$ | RC circuit time constant | s | Time for discharge to 37% of initial value |
| $\ln Q = \ln Q_0 - t/RC$ | Log-linear RC discharge | Unitless | Gradient of plot = $-1/RC$ |
| $F = BIl\sin\theta$ | Force on current-carrying conductor | N | θ = angle between I and B |
| $F = Bqv\sin\theta$ | Force on moving charged particle | N | Reverse direction for negative charges |
| $\|E\| = N\Delta\phi/\Delta t$ | Induced emf (Faraday's law) | V | Average emf over time interval Δt |

## What's next

Once you have mastered electric and magnetic fields, you will be ready to tackle the final Unit 4 topic: Nuclear and Particle Physics, where you will apply field concepts to particle acceleration, deflection, and detection. This topic also forms a critical foundation for Unit 5 content including gravitational fields, astrophysics, and nuclear decay, so solidifying your understanding of field line, potential, and energy rules now will reduce your revision load later. Prioritize practicing past paper questions focused on RC log-linear plots and electromagnetic induction direction questions, as these are high-frequency exam questions that often trip up students. You should also review Core Practical 11 methodology to prepare for practical exam questions on capacitor time constant measurement.

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