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Moving Charges and Magnetism

The field of a wire, a loop and a solenoid, the force on a moving charge, and the galvanometer conversions. Directions decide many answers.

Questions in the bank
172
q/paper in 2025–26
1.15
Numeric answer
28%
Notes pages
7

Tier: Core

When you’ll see it

A current making a field at a point, a charge moving through B or through crossed E and B, a wire or coil in a field, or a galvanometer turned into a meter.

How this chapter is tested

Moving Charges and Magnetism is a core chapter, set about once a paper. Its largest part finds the field a current makes; most of the rest finds the force a field puts on a moving charge or on a wire, and the last part turns the torque on a coil into a meter.

Every field question is a sum of a few standard pieces: (μ₀I/4πd)(sin α₁ + sin α₂) for a straight piece, μ₀Iθ/4πR for an arc, μ₀NI/2R at the centre of a coil, μ₀nI inside a solenoid. Knowing these by heart saves the most time. Decide the direction of each piece, into or out of the page, before adding.

Marks are lost on a direction or a factor: μ₀I/2πd used for a wire that ends at the point, an angle measured from the plane of a coil instead of its axis, an electron's force left with a proton's sign, or turns per centimetre never turned into turns per metre. The meter pages connect to Current Electricity, and the moment and torque of a coil return in Magnetism and Matter.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Straight wires and arcs

    (μ₀I/4πd)(sin α₁ + sin α₂) for a straight piece, μ₀I/2πd for a long wire, μ₀Iθ/4πR at the centre of an arc; radial pieces give nothing.

  • Circular loops and coils

    μ₀NI/2R at the centre; on the axis the field falls as R³/(R² + x²)^(3/2), so most questions are a ratio to the centre value.

  • Ampère's law

    The line integral of B equals μ₀ times the enclosed current: B grows with r inside a solid wire, is zero outside a coaxial cable, and is μ₀nI inside a solenoid.

  • Lorentz force and crossed fields

    F = q(E + v × B); the magnetic part never changes the speed; a velocity selector passes v = E/B whatever the charge or mass.

  • Circular and helical paths

    r = mv/qB and T = 2πm/qB, the same at every speed; the pitch uses the part of v along B; a cyclotron particle gains energy twice a turn.

  • Forces and torques on wires

    F = IL × B, a bent wire acting like its chord; parallel currents μ₀I₁I₂/2πd per metre, like currents attracting; torque NIAB sin θ with θ from the axis.

  • Galvanometer and meters

    Deflection proportional to current; a shunt S = IgG/(I − Ig) in parallel makes an ammeter; a series resistance V/Ig − G makes a voltmeter.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • The long-wire value for a wire that ends

    At a point level with the end of a semi-infinite wire the field is μ₀I/4πd, half the long-wire value μ₀I/2πd.

  • Angle from the plane

    In τ = NIAB sin θ, θ is between the coil's normal and B. When the angle with the plane is given, use its complement.

  • An electron with a proton's sign

    For an electron the force is along −(v × B). Stopping at the direction of v × B reverses every electron answer.

  • Turns per centimetre

    In B = μ₀nI, n is turns per metre. Leaving it per centimetre makes B a hundred times too small.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Moving Charges and Magnetism notes

Drill every Moving Charges and Magnetism question

172 questions from the bank, across 7 subtopics.

Drill the 172 questions

Drill one subtopic at a time

The 7 subtopics, in teaching order.

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