Unit 4: Electric and Magnetic Fields

This guide covers sub-topic 4.4 Electric and Magnetic Fields, the second of three sub-topics in Unit 4: Further Mechanics, Fields and Particles, from the Pearson Edexcel International Advanced Level in Physics (YPH11), Issue 3 specification. This topic is commonly studied using applications such as communications and display technology.

Before studying this

This topic builds on Unit 2’s electric circuits content (current, p.d., resistance) and assumes comfort with exponential functions and logarithms.

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL A LEVEL PHYSICS (YPH11) — Sub-topic 4.4

Candidates will be assessed on their ability to: understand that an electric field (force field) is a region where a charged particle experiences a force; understand that electric field strength is defined as E = F/Q; use the equation F = Q₁Q₂/4πε₀r² for the force between two charges; use E = Q/4πε₀r² for the electric field due to a point charge; know and understand the relation between electric field and electric potential; use E = V/d for a field between parallel plates; use V = Q/4πε₀r for a radial field; draw and interpret diagrams using field lines and equipotentials for radial and uniform electric fields; understand that capacitance is defined as C = Q/V; use W = ½QV for the energy stored by a capacitor, derive it from the area under a graph of p.d. against charge stored, and derive and use W = ½CV² and W = Q²/2C; draw and interpret charge and discharge curves for resistor-capacitor circuits and understand the significance of the time constant RC; CORE PRACTICAL 11: use an oscilloscope or data logger to display and analyse the p.d. across a capacitor as it charges and discharges through a resistor; use Q = Q₀e^(−t/RC) and derive and use related equations for exponential discharge, I = I₀e^(−t/RC) and V = V₀e^(−t/RC), and the corresponding log equations; understand and use magnetic flux density B, flux φ and flux linkage Nφ; use F = Bqvsinθ and apply Fleming’s left-hand rule to charged particles moving in a magnetic field; use F = BIlsinθ and apply Fleming’s left-hand rule to current-carrying conductors; understand the factors affecting the e.m.f. induced in a coil when there is relative motion between the coil and a permanent magnet; understand the factors affecting the e.m.f. induced in a coil when there is a change of current in another coil linked with this coil; and understand how to use Faraday’s law to determine the magnitude of an induced e.m.f. and use the equation combining Faraday’s and Lenz’s laws, ε = −N(dφ/dt).

Electric fields

An electric field is a region where a charged particle experiences a force. Electric field strength is E = F/Q. Between two point charges, Coulomb’s law gives the force:

F = Q1 Q2 / 4πε0 r²

and the field due to a single point charge is E = Q/4πε₀r². Electric field and electric potential are related — potential falls in the direction the field points, and the field strength is (minus) the potential gradient. For a uniform field between parallel plates, E = V/d; for a radial field, V = Q/4πε₀r. Field lines and equipotentials (surfaces of constant potential, always perpendicular to field lines) are used to represent both radial and uniform fields.

Capacitors

Capacitance is defined as C = Q/V. The energy stored by a charged capacitor is W = ½QV — derivable as the area under a graph of p.d. against charge stored — and equivalently W = ½CV² or W = Q²/2C.

When a capacitor discharges through a resistor, charge, current and p.d. all fall exponentially:

Q = Q0 e^(-t/RC)
I = I0 e^(-t/RC)
V = V0 e^(-t/RC)

The product RC is the time constant, the time for the quantity to fall to 1/e (about 37%) of its initial value. Taking logs of these equations gives straight-line forms (e.g. lnQ = lnQ₀ − t/RC), useful for determining RC graphically. CORE PRACTICAL 11 uses an oscilloscope or data logger to display and analyse the p.d. across a capacitor as it charges and discharges through a resistor.

Magnetic fields and electromagnetic induction

Magnetic flux density B, flux φ and flux linkage Nφ describe a magnetic field’s strength and its interaction with a coil of N turns. The force on a charged particle moving in a magnetic field is:

F = Bqv sinθ

with direction given by Fleming’s left-hand rule. The force on a current-carrying conductor in a field is similarly F = BIl sinθ, again using Fleming’s left-hand rule.

Electromagnetic induction: an e.m.f. is induced in a coil when there is relative motion between the coil and a permanent magnet, or when current changes in another coil linked with it. Faraday’s law relates the magnitude of the induced e.m.f. to the rate of change of flux linkage, and combined with Lenz’s law (which gives the direction, opposing the change that causes it):

ε = −N(dφ/dt)

Worked example. A capacitor of capacitance 220 μF is charged to 9.0 V and then discharged through a 47 kΩ resistor. Find the time constant, and the p.d. across the capacitor after one time constant.

Time constant RC = (220 × 10⁻⁶) × (47 × 10³) = 10.34 s (≈ 10 s).

After one time constant, V = V₀e⁻¹ = 9.0 × 0.368 = 3.3 V.

Common mistakes

Confusing electric field strength (force per unit charge) with electric potential (energy per unit charge) — they are related but not the same physical quantity. Using W = ½QV when Q and V given are not both the final charge and final p.d. reached (the ½ accounts for the fact that p.d. rises from zero as the capacitor charges). Forgetting that Fleming’s left-hand rule applies to the force on a current or moving charge, while the right-hand rule (not examined here) is typically used for the field around a current. Mixing up flux (φ, through one turn) with flux linkage (Nφ, through all N turns of a coil).

Quick revision checklist

• Use E = F/Q, Coulomb’s law F = Q1Q2/4πε0r², and E = Q/4πε0r².
• Relate electric field and potential; use E = V/d (uniform) and V = Q/4πε0r (radial).
• Use C = Q/V and the three forms of capacitor energy (½QV, ½CV², Q²/2C).
• Interpret RC charge/discharge curves and describe CORE PRACTICAL 11.
• Use the exponential decay equations and their log forms for RC circuits.
• Use F = Bqvsinθ and F = BIlsinθ with Fleming’s left-hand rule.
• Explain the factors affecting induced e.m.f. and use ε = −N(dφ/dt).

Related resources

• Unit 4: Further Mechanics — the previous sub-topic
• Unit 4: Nuclear and Particle Physics — the next sub-topic
• Unit 2: Electric Circuits — foundational circuits content this topic builds on
• Pearson Edexcel International A Level Physics hub

This guide is intended to support, not replace, engagement with the official Pearson Edexcel specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.