IMAT Physics · Formula sheet

Magnetism formulas

6 formulas, 1 reference table and 10 common traps for IMAT Physics Magnetism, grouped by subtopic.

Magnets, Magnetic Fields and the Force on Currents and Charges

The magnetic field of a straight wire and of a solenoid

Field of a long straight wire and of a solenoid

B_{\text{wire}} = \frac{\mu_0 I}{2\pi r} \qquad B_{\text{solenoid}} = \mu_0 \frac{N}{L} I

$B$ magnetic field strength, in T
$I$ current, in A
$r$ distance from the wire, in m
$N/L$ turns per metre of the solenoid
$\mu_0$ $4\pi \times 10^{-7}\ \text{T m/A}$

The force on a current-carrying wire in a magnetic field

Force on a wire

F = B I L \sin\theta

$F$ force, in N
$B$ magnetic field, in T
$I$ current, in A
$L$ length of wire in the field, in m
$\theta$ angle between the wire and the field

The force on a moving charge: F = qvB sinθ

Force on a moving charge

F = q v B \sin\theta

$q$ charge, in C
$v$ speed, in m/s
$B$ magnetic field, in T
$\theta$ angle between the velocity and the field

Circular motion of a charged particle in a magnetic field

Radius and period of the circle

r = \frac{m v}{q B} \qquad T = \frac{2\pi m}{q B}

$r$ radius of the circle, in m
$m$ mass of the particle, in kg
$v$ speed, in m/s
$T$ time for one revolution, in s

Magnets, poles, field lines and the Earth's field

Object near a bar magnet	Force it feels	Reason
Unmagnetised iron, nickel or cobalt	Attraction to either pole, never repulsion	The magnet induces an opposite pole in the near end
Another magnet (e.g. magnetised steel)	Attraction or repulsion, depending on which poles face	Like poles repel, unlike poles attract
Copper, aluminium, wood, plastic	Practically none	Not ferromagnetic
An electrically charged object at rest	No magnetic force	A magnetic field acts only on moving charges

Common traps

Attraction does not prove an object is a magnet

Any piece of iron, nickel or cobalt is attracted by a magnet, magnetised or not. Only repulsion shows the object is a magnet. A charged but non-magnetic object at rest feels no magnetic force at all.

A wire's field falls as 1/r, not 1/r²

The field of a long straight wire is proportional to

1/r

: twice as far, half the field. The inverse square law belongs to point charges and point masses. Using it for a wire gives the wrong option every time.

No force when the current runs along the field

The force depends on

\sin\theta

. A wire lying parallel to the field feels no force at all, however large the current or the field. The force is never along the field lines; it is always at right angles to them.

A magnetic field cannot change a particle's speed

The magnetic force is always at right angles to the velocity, so it does no work. The kinetic energy and speed stay the same; only the direction turns. To speed a charge up you need an electric field.

Constant speed is not constant velocity

In a magnetic field the speed stays fixed but the direction turns all the time, so the velocity (a vector) is always changing. Any statement that the particle keeps the same velocity after entering the field at right angles is false.

Electromagnetic Induction, Generators and Transformers

Learn this subtopic in the notes

Magnetic flux and Faraday's law of induction

Faraday's law

\Phi = B A \cos\theta \qquad \varepsilon = N \frac{\Delta \Phi}{\Delta t}

$\Phi$ magnetic flux through one turn, in Wb
$N$ number of turns of the coil
$\Delta t$ time taken for the change, in s
$\varepsilon$ average induced e.m.f., in V

Generators and transformers

Ideal transformer

\frac{V_s}{V_p} = \frac{N_s}{N_p} \qquad V_p I_p = V_s I_s

$V_p, V_s$ primary and secondary voltages (AC), in V
$N_p, N_s$ number of turns on the primary and secondary coils
$I_p, I_s$ primary and secondary currents, in A

Common traps

A strong field alone induces nothing

Induction needs a change of flux. A coil in a huge but steady field, with nothing moving, has no induced e.m.f. What matters is how fast the flux changes, not how big it is.

Thicker wire does not raise the induced e.m.f.

The e.m.f. depends on the number of turns, the field, the area and the speed of change. Thicker wire lowers the resistance, so more current flows for the same e.m.f., but the e.m.f. itself is unchanged.

The induced current opposes the change, not the field

Lenz's law opposes the change of flux. If the flux through a coil is falling, the induced current tries to keep it up, making a field in the same direction as the original one. Reversing either the pole or the direction of motion reverses the current; reversing both leaves it unchanged.

A transformer cannot increase power

A step-up transformer raises the voltage but lowers the current by the same factor, so the power out is at most the power in. An option where both voltage and current go up, or where power is gained, is always wrong.

Transformers do not work on DC

Induction needs a changing flux. A steady direct current makes a steady flux in the core, so the secondary has no e.m.f. once the current has settled.

Magnetism formulas

Magnets, Magnetic Fields and the Force on Currents and Charges

The magnetic field of a straight wire and of a solenoid

The force on a current-carrying wire in a magnetic field

The force on a moving charge: F = qvB sinθ

Circular motion of a charged particle in a magnetic field

Magnets, poles, field lines and the Earth's field

Common traps

Electromagnetic Induction, Generators and Transformers

Magnetic flux and Faraday's law of induction

Generators and transformers

Common traps

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