Speed Maths LAB
EXP-001
Module 6
OCR A H556 · 6.3.1-6.3.2

Magnetic Fields

Five benches. Each one turns an equation into something you can poke. Drag the sliders, flip the current, and watch what the field does. The colours are the same everywhere:

magnetic field B conventional current I / velocity v force F ⊙ out of the page   ⊗ into the page
What clicked

The wire is catapulted from the strong side to the weak side.

Bench 1
6.3.1(c)

The field around a wire

You're looking straight down the wire. The field makes closed circles around it. Move your pointer over the picture: the compass needle shows which way a north pole would be pushed there. Near the wire the circles crowd together (strong field); further out they spread (\(B \propto 1/r\)).

In the exam
  • Right-hand grip rule: thumb along the conventional current, fingers curl in the field direction.
  • Out of the page: anticlockwise. Into the page: clockwise.
  • Draw circles getting further apart as you go out, with arrows on them.
Bench 2
why F = BIL exists

Why the wire gets pushed

Put the wire between two poles. Its circular field adds to the magnet's field on one side and cancels it on the other. Field lines behave like stretched elastic bands: crowded lines on one side, sparse lines on the other, so the wire is catapulted from the strong side towards the weak side. That push is the motor effect. The shading shows how strong the total field is.

Set the current to 0: the lines go straight across and there's no force. Turn it up: the bending gets stronger, and so does the force.

In the exam
  • Force direction: Fleming's left-hand rule. You don't draw the combined field unless asked; it's here so the rule makes sense.
  • "Force on the wire" and "force on the magnet" are equal and opposite (Newton's third law). That's exactly what the balance practical measures.
Bench 3
6.3.1(e)

F = BIL sin θ: only the cross-ways part counts

The field runs left to right across the page. Rotate the wire. Only the part of the wire that cuts across the field (the dashed component, \(L\sin\theta\)) feels a force. Parallel to the field, there's nothing to push against, so \(F = 0\). Here the force is always into or out of the page.

In the exam
  • θ is the angle between the wire and the field. Max force at 90°, zero when parallel.
  • \(B = F/(IL)\): flux density is the force per unit current per unit length on a wire at 90° to the field. \(1\ \text{T} = 1\ \text{N}\,\text{A}^{-1}\,\text{m}^{-1}\).
  • Check: \(B = 0.080\ \text{T}\), \(I = 4.0\ \text{A}\), \(L = 5.0\ \text{cm}\) at 90° gives \(F = 0.016\ \text{N}\). Try it on the sliders.
Bench 4
6.3.1(d)

Fleming's left-hand rule trainer

First finger = Field (N to S). SeCond finger = Current (conventional). ThuMb = Motion / force. Pick where the force points. The first one is the question you just got right.

0 / 0
Bench 5
6.3.2(a)(b)

A charge in a field goes round in circles

The field is into the page everywhere. The magnetic force BQv is always at 90° to the velocity. It never speeds the particle up or slows it down, it only turns it, so the speed stays constant and the path is a circle. Change the sliders and watch r. Then watch the orbit time: it doesn't change when you change the speed.

In the exam
  • Why a circle: "the force is at right angles to the velocity, so no work is done and the speed is constant". Say force, not acceleration, and velocity, not speed.
  • \(BQv = mv^2/r\), so \(r = mv/(BQ)\). Faster or heavier: bigger circle. Stronger field or bigger charge: smaller circle.
  • \(T = 2\pi r/v = 2\pi m/(BQ)\): no v in it. Faster particles take bigger circles in the same time.