AP Inter 2nd Year Physics Notes Chapter 8 Magnetism and Matter

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AP Inter 2nd Year Physics Notes 8th Lesson Magnetism and Matter

→ Load stone is a natural magnet. It is ore of Iron magnitite. Load stone means leading stone.

→ The magnetic field lines of a magnet (or a solenoid) form continuous closed loops.

→ Magnetic dipole moment m associated with a current loop is m = NIA where N is the no. of turns in the loop. I the current and A the area vector.

→ Magnitude of the magnetic moment of the solenoid is m = n(2l) I (πa²)

→ Axial magnetic field of a bar magnet B_A = \(\frac{\mu_0}{4 \pi} \frac{2 \mathrm{~m}}{\mathrm{r}^3}\)

→ Torque on the dipole (needle) in a uniform magnetic field is τ = m × B.

→ Equtorial field of a bar magnet B_E = \(\frac{\mu_0}{4 \pi} \frac{\mathrm{m}}{\mathrm{r}^3}\)

→ Gauss’s Law in Magnetism : The net magnetic flux through any closed surface is zero.
\(\int_S\) B. ds = 0

→ Magnetic meridian of a place as the vertical plane which passes through the imaginary line joining the magnetic north and the south poles.

→ The angle between the true geographic north and the north shown by a compass needle is called declination.

→ The angle between the direction of the total earth’s magnetic intensity and the horizontal line in the magnetic meridian is known as the angle of dip or the angle of inclination.

→ Magnetic moment per unit volume is called magnetisation. M = \(\frac{m_{n e t}}{V}\). It’s unit is Am^-1 and its dimensions L^-1A.

→ At 300k, negative dia magnetic substances are Bismuth, copper, diamond, gold, lead, mercury, nitrogen (STP), silver, silicon.

→ At 300 k, positive paramagnetic substances are Aluminium, Calcium, Chromium, Lithium, Magnesium, Niobium, Oxygen (STP), Platinum, Tungasten.

→ For Liamagnetic substances, -1 ≤ χ <0; 0 ≤ μ_r < 1; μ < μ₀

→ For Paramagnetic substances, 0 < χ < ε; 1 < μ_r < 1 + ε; μ > μ₀

→ For Ferromagnetic substances χ < < 1; μ_r > > 1; μ > > μ₀

→ The magnetisation of a paramagnetic material is inversely porportional to the absolute temperature T.
M = \(\frac{\mathrm{CB}_0}{\mathrm{~T}}\) or equivalently, χ = C \(\frac{\mu_0}{\mathrm{~T}}\)

→ As the field is increased or the temperature is lowered on the paramagnetic sample, the magnetisation increases until it reaches the saturation value M_s, at which point all the dipoles are perfectly aligned with the field.

→ Macroscopic volume of a ferromagnetic material from 10^-6 cm³ to 10^-2 cm³ is called domain.

→ The domain size is 1mm and the domain contains about 10¹¹ atoms.

→ In some ferromagnetic materials the magnetisation persists. Such materials are called hard magnetic materials or hard ferromagnetic. For ferromagnetic materials, μ_r > 1000.

→ The temperature of transition from ferromagnetic to paramagnetism is called the curie temperature T_C.

→ The lagging of I and B behind H is called, hysterisis.

→ The value of I for which H = 0 is called retentivity.

→ The value of magnetising force required to reduce I is zero in reverse direction of H is called coercivity.

→ Electromagnets are used in electric bells, loudspeakers and telephone diaphragms.

Formulae

→ Coulombs Law, F = \(\frac{\mu_0}{4 \pi} \frac{\mathrm{m}_1 \mathrm{~m}_2}{\mathrm{r}^2}=10^{-7} \times \frac{\mathrm{m}_1 \mathrm{~m}_2}{\mathrm{r}^2}\)

→ Magnetic dipole \(\overrightarrow{\mathrm{M}}=\mathrm{m}(\overrightarrow{2 l})\)

→ Magnetic moment of current loop is \(\overrightarrow{\mathrm{M}}=\overrightarrow{\mathrm{IA}}\)

→ Magnetic moment due to orbital motion μ_l = \(\mathrm{n}\left(\frac{\mathrm{eh}}{4 \pi \mathrm{m}_{\mathrm{e}}}\right)\)

→ Bohr magneton μ_B = \(\frac{e h}{4 \pi \mathrm{m}_{\mathrm{e}}}\)

→ \(\overrightarrow{\mathrm{B}}_{\text {axial }}=\frac{\mu_0}{4 \pi} \frac{2 \overrightarrow{\mathrm{m}} \mathrm{r}}{\left(\mathrm{r}^2-l^2\right)^2}\)

→ For a short dipole, B_axial = \(\frac{\mu_0}{4 \pi} \frac{2 \mathrm{~m}}{\mathrm{r}^3}\)

→ \(\overrightarrow{\mathrm{B}}_{\mathrm{e}}=\frac{\mu_0}{4 \pi} \frac{\overrightarrow{\mathrm{m}}}{\left(\mathrm{r}^2+l^2\right)^{3 / 2}}\) for short magnet B_e = \(\frac{\mu_0}{4 \pi} \frac{\mathrm{m}}{\mathrm{r}^3}\)

→ Magnetic field at any point due to short magnetic dipole is B = \(\frac{\mu_0}{4 \pi} \frac{M \sqrt{3 \cos ^2 \theta+1}}{r^3}\)

→ Torque \(\vec{\tau}=\overrightarrow{\mathrm{m}} \times \overrightarrow{\mathrm{B}}\)

→ P.E. of a bar magnet placed in a magnetic field is U = =mB sin θ = \(-\overrightarrow{\mathrm{m}} \times \overrightarrow{\mathrm{B}}\)

→ Gauss’s law in magnetism \(\oint \mathrm{B} \cdot \mathrm{d} \overrightarrow{\mathrm{s}}\) = 0

→ Magnetic intensity H = \(\frac{\mathrm{B}_0}{\mu_0}\)

→ Intensity of magnetisation is I = \(\frac{\mathrm{M}}{\mathrm{v}}=\frac{\mathrm{m} \times 2 l}{\mathrm{~A} \times 2 l}=\frac{\mathrm{m}}{\mathrm{A}}\)

→ Magentic flux Φ = \(\overrightarrow{\mathrm{B}} \cdot \Delta \overrightarrow{\mathrm{S}}\)

→ Magnetic susceptibility χ = \(\frac{\mathrm{I}}{\mathrm{H}}\)

→ Magnetic permeability μ = \(\frac{\mathrm{B}}{\mathrm{H}}\)

→ μ = μ₀ (1 + χ_m)
Also μ_r = 1 + χ_m

→ Curies law is χ_m ∝ \(\frac{1}{T}\)
χ_mT = constant