Magnetism

 

The property of magnet to attract another magnet and magnetic materials is termed as magnetism.

A magnet has directive property, i.e if a magnet is freely suspended it will come to rest in a position close to north-south direction.

Pole : Pole of magnet is where attracting power of magnet is maximum. Pole strength is vector quantity.

The force of attraction or repulsion $F$ between two magnetic poles of strength $m_1$ and $m_2$ separated by distance $r$ is directly proportional to the product of pole strengths and inversely proportional to the square of distance between their centers.

$F=k \dfrac{m_1m_2}{r^2}$ where $k$ is magnetic force constant.

Repulsion is a sure test of magnetism.

On heating magnets, molecular magnets acquire some kinetic energy. Some of the molecules may get back to the close chain arrangement, so magnetism of specimens would reduce heating.

S.I unit of magnetic field strength is tesla. $Cgs$ unit is gauss. $1G=10^{-4} T$

A line perpendicular to the magnetic length which bisects it is called its magnetic equator.

$\dfrac{\text{Magnetic length}}{\text{Geometrical length}}=0.85$

Uniform magnetic field is a point at which magnetic field intensity is the same at all the points.

The imaginary line joining the magnetic north and south poles of the earth’s magnet or any magnet is called its magnetic axis.

The imaginary line joining the geographical north and south poles of the earth is called the geographical axis.

The angle between the geographical meridian and the magnetic meridian is called declination.

Angle made by a freely suspended magnet with a horizontal component of the earth magnetic field at a place is called angle of dip.

The angle of dip in magnetic meridian is called real dip or true dip and the angle of dip at other planes is called apparent dips.

A magnetic device used to measure the angle of dip is called dip circle.

$\textbf{Magnetic Dipole}$:

If the $N$ pole and $S$ pole of a magnet are separated by a very small distance then it is called a magnetic dipole.

Magnetic dipole moment $=m * 2l$

Direction of magnetic dipole moment is from south to north.

Two magnets are inclined at an angle $\alpha$ then,

$\textbf{Resultant dipole moment}$

$M=\sqrt{M_1^2+M_2^2+2M_1} M_2 cos\alpha$

Above case is condition when two likes pole together, if incase of two unlike pole together replace $2$ with $-2$.

$\textbf{Magnetic field Strength due to Bar magnet}$: $\textbf{Tan A position / End on position}$:

$B_a=\dfrac{µ}{4\pi} \dfrac{2Md}{(d^2-l^2 )^2}$

The direction of $B_a$ is along $SN$, for short bar magnet $B=\dfrac{µ}{4\pi} \dfrac{2M}{d^3}$

$\textbf{Tan B position/ Broad Side Position}$

$B_e==\dfrac{µ}{4\pi} \dfrac{2Md}{(d^2+l^2 )^{3/2}}$

The direction of $B_e$ is along $NS$, for short bar magnet $B=\dfrac{µ}{4\pi} \dfrac{M}{d^3}$ ($B_a=2B_e$)

$\textbf{Torque on a Bar magnet in a magnetic field}$.

$Τ=mB.2lsin\alpha$

$τ=MBsin\alpha$

Torque is minimum for $0$ degree and maximum for $90$ degree.

$\textbf{Potential Energy}$:

$U=-MBcos\alpha$

where $\alpha$ is the angle between $M$ and $B$.

$\to$ For stable equilibrium angle between them must zero and for unstable equilibrium angle between them is $10$ degree.

$\to$ Work done in displacing dipole from $\alpha_1$ to $\alpha_2$ is

$W=MB(cos α_1 -cos α_2)$

$\to$ Work done in rotating dipole from equilibrium position ($0$) through angle $\alpha$ is

$W=MB(1 -cos \alpha)$

Magnetic material

$\text{Properties}$:

$\to$ $\textbf{Magnetising Field(H)}$ :Field in which material is placed for magnetization .

$\to$ $\textbf{Intensity of magnetization(I)}$ When a magnetic material is placed in the magnetization field produces a dipole moment per unit volume is known as I .

$\to$ $\textbf{Magnetic Susceptibility}$: The ease at which magnet can be magnetized.

Materials

$\text{Diamagnetic material}$:

Poor magnetization in the opposite direction when placed in the magnetic field.

$\textbf{Paramagnetic material}$:

Poor magnetization in the same direction when placed in an external magnetic field.

$\textbf{Ferromagnetic}$:

Strong magnetization in the same direction when placed in a magnetic field.

$\textbf{Magnetic Hysteresis}$.

$\to$ Lagging of B behind H is called hysteresis.

$\to$ Coercivity is a measure of the magnetising field required to destroy the residual magnetism of a specimen.

$\to$ Retentivity of a specimen is a measure of magnetic field remaining in the specimen when magnetizing field is removed.

$\to$ Steel is used in permanent magnet(High Coercivity and Low retentivity).

$\textbf{Vibration Magnetometer}$

$\textbf{Time period}$:

$T=2\pi \sqrt{\dfrac{I}{MH}}$

I=Moment of inertia ,M=Magnetic moment of magnet,

H=Horizontal component of earth mag field.

I=moment of inertia

$\textbf{Comparison of Horizontal Components of Magnetic field}$:

$\dfrac{T1}{T2}=\sqrt{\dfrac{H2}{H1}}$

$\dfrac{H2}{H1}=\dfrac{T1^2}{T2^2}$

$\textbf{Comparison of Magnetic moment}$:

$\dfrac{M2}{M1}=\dfrac{T1^2}{T2^2}$

$\textbf{Comparison of magnetic moments of two magnets of unequal sizes and masses}$:

$\dfrac{M2}{M1}=\dfrac{T2^2+T1^2}{T2^2-T1^2}$

$\dfrac{T1}{T2}=\sqrt{\dfrac{M1-M2}{M1+M2}}$

Read and Digest

Magnetic field doesn’t interact with charge at rest.

Magnetism is caused by both spin motion and orbital motion of electrons but majoris spin motion.

Pole strength is independent of length but depends on the cross sectional area of the bar magnet.

At neutral points $H=0$, so $T=INF$ and $f=0$

Magnetic moment of noble gases$=0$

$\textbf{Diamagnetism}$ is the universal property of all substances.

$\textbf{At curie temperature}$ Ferromagnetic becomes para magnets.

If a magnetized wire having dipole moment M is bent at an angle α then dipole moment of arc is

$M'=\dfrac{Msin\alpha}{\alpha}$

If a bar magnet is cut into two equal parts:

$\textbf{Perpendicular to length}$:

Pole strength remains the same, magnetic dipole moment(M) becomes half.

$\textbf{Parallel to length}$:

Pole strength becomes half and dipole moment also becomes half.