JEE Mains Physics · Formula sheet

Magnetism and Matter formulas

5 formulas, 2 reference tables and 17 common traps for JEE Mains Physics Magnetism and Matter, grouped by subtopic.

Bar Magnets and Magnetic Dipoles

Magnetic dipole moment and the field of a bar magnet

Short magnet: axial field, equatorial field, axial potential

B_{axial} = \frac{\mu_0}{4\pi}\frac{2M}{r^{3}} \qquad B_{eq} = \frac{\mu_0}{4\pi}\frac{M}{r^{3}} \qquad V_{axis} = \frac{\mu_0}{4\pi}\frac{M}{r^{2}}

Torque and potential energy of a dipole in a uniform field

Dipole in a uniform field

\tau = MB\sin\theta \qquad U = -MB\cos\theta \qquad W = MB(\cos\theta_1 - \cos\theta_2)

Common traps

Bending keeps the pole strength, not the moment

A bent magnet has the same pole strength but its poles are closer together, so its moment falls. A semicircle gives 2M/π, not M.

The equatorial field points opposite to the moment

On the axis the field of a short magnet points along M; on the equator it points opposite to M. The direction matters when this field is added to another.

Using the axial formula at an equatorial point

The factor 2 belongs to the axis only. Check where the point lies before choosing the formula: a point on the perpendicular bisector is equatorial.

Dropping the minus sign in the energy

The potential energy is −MB cos θ. At angles below 90° it is negative, and an option with the right size but a positive sign is a deliberate trap.

Reading the plane of a coil as its moment

A coil's moment is along the normal to its plane. A plane perpendicular to B means the moment is along B, which is the stable position, not the position of largest torque.

Work is a difference of cosines, not of angles

Turning from 0° to 60° needs MB(1 − ½) = MB/2, not a third of the work for 0° to 180°. Always subtract the two values of cos θ.

The Earth's Field: Dip and Oscillating Magnets

Learn this subtopic in the notes

Components of the earth's field and the angle of dip

Components, and dip in a plane at α to the meridian

B_H = B\cos\delta \qquad B_V = B\sin\delta \qquad \tan\delta' = \frac{\tan\delta}{\cos\alpha} \qquad \cot^{2}\delta = \cot^{2}\delta_1 + \cot^{2}\delta_2

Horizontal component: neutral points and oscillating magnets

Oscillation period and the frequency at two places

T = 2\pi\sqrt{\frac{I}{MB_H}} \qquad \frac{n_1^{2}}{n_2^{2}} = \frac{B_1\cos\delta_1}{B_2\cos\delta_2}

Common traps

Swapping sine and cosine

The horizontal component is B cos δ and the vertical one is B sin δ. At a large dip the field is nearly vertical, so the vertical part is the larger one.

Geographic meridian in place of magnetic

The dip relations use the angle from the magnetic meridian. They give the same answer for the geographic meridian only when the declination is zero.

Using the total field for the period

A needle swinging in a horizontal plane responds to B cos δ only. When the dip changes from place to place, the cos δ factor must go into the comparison.

Oscillations per minute are a frequency

The square of the number of oscillations per minute is proportional to B_H. The square of the period is inversely proportional to it. Mixing the two inverts the ratio.

Magnetic Properties of Materials and Hysteresis

Learn this subtopic in the notes

Magnetic intensity, susceptibility and permeability

Magnetising a material

M = \chi H \qquad B = \mu_0(H + M) = \mu_0\mu_r H \qquad \mu_r = 1 + \chi \qquad \frac{\Delta B}{B_0} = \chi

Diamagnetic, paramagnetic and ferromagnetic materials

Property	Diamagnetic	Paramagnetic	Ferromagnetic
Susceptibility χ	Small, negative: −1 ≤ χ < 0	Small, positive	Very large, positive
Relative permeability μᵣ	Slightly less than 1	Slightly more than 1	Much greater than 1
Atomic moments	None; the field induces a moment opposite to itself	Permanent, randomly oriented without a field	Permanent, aligned within domains
In a non-uniform field	Moves from strong to weak field	Moves from weak to strong field, weakly attracted	Strongly attracted
Effect of temperature	χ does not depend on temperature	χ = C/T (Curie's law)	Paramagnetic above the Curie temperature
M against H	Straight line, negative slope	Straight line, small positive slope	Curved, saturates, shows hysteresis
Examples	Bismuth, copper, water, superconductors	Aluminium, sodium, oxygen	Iron, cobalt, nickel

Hysteresis and choosing a magnetic material

Use	Material	Retentivity	Coercivity	Hysteresis loop
Electromagnet core	Soft iron	Low	Low	Narrow, small area
Transformer core	Soft iron, laminated	Low	Low	Narrow, so little energy is lost each cycle
Permanent magnet	Steel, alnico, cobalt steel	High	High	Wide, large area

Common traps

Fraction and percentage

Filling a solenoid raises B by the fraction χ. The percentage rise is 100χ. Options often offer both, one of them a hundred times off.

Relative permeability and susceptibility differ by one

μᵣ = 1 + χ. For a strongly magnetic material the difference hardly matters, but for a susceptibility near zero, using χ in place of μᵣ throws the answer away.

Calling a strongly attracted material paramagnetic

Paramagnets are attracted only weakly. Strong attraction is the mark of a ferromagnet.

Getting the direction of drift backwards

A paramagnet moves from a weak field towards a strong one. A diamagnet moves the other way, from strong to weak.

Letting diamagnetism depend on temperature

Diamagnetism comes from moments induced in the electron orbits, not from aligning permanent moments, so heating does not change it. Only paramagnets and ferromagnets above the Curie point follow a temperature law.

Swapping retentivity and coercivity

Retentivity is a value of B, read where the loop cuts the B-axis. Coercivity is a value of H, read where it cuts the H-axis.

Wanting a large retentivity in an electromagnet

An electromagnet must lose its magnetism when the current stops. Soft iron is chosen for its high permeability and its low retentivity and coercivity.

Magnetism and Matter formulas

Bar Magnets and Magnetic Dipoles

Magnetic dipole moment and the field of a bar magnet

Torque and potential energy of a dipole in a uniform field

Common traps

The Earth's Field: Dip and Oscillating Magnets

Components of the earth's field and the angle of dip

Horizontal component: neutral points and oscillating magnets

Common traps

Magnetic Properties of Materials and Hysteresis

Magnetic intensity, susceptibility and permeability

Diamagnetic, paramagnetic and ferromagnetic materials

Hysteresis and choosing a magnetic material

Common traps

More JEE Mains Physics formula sheets