Class 12 Magnetism and Matter Important Notes

The chapter highlights some commonly known ideas about magnetism:

• The Earth is like a giant magnet. Its magnetic field points approximately from the geographic south to the north.
• A freely suspended bar magnet aligns itself in north-south direction. The north pole points towards geographic north, and south pole points towards geographic south.
• Like poles repel each other, whereas unlike poles attract.
• Magnetic monopoles (isolated north or south poles) do not exist. Breaking a bar magnet results in two smaller magnets, each with its own north and south poles.
• Magnets can be made from iron and its alloys.

Materials can be classified based on their magnetic properties:

• Diamagnetic Materials: These materials are weakly repelled by magnetic field. They have negative magnetic susceptibility, due to which they lose magnetization as soon as the external field is removed. Some examples of diamagnetic materials include bismuth, copper, and water.
• Paramagnetic Materials: JEE Main entrance exam ask questions around these types of materials. These are weakly attracted by the magnetic field. They have positive magnetic susceptibility and they also lose magnetization as soon as the external field is removed. Examples of paramagnetic materials are aluminium, sodium, and oxygen. 
• Ferromagnetic Materials: These are strongly attracted by a magnetic field, and they still have magnetization even after removing the external field. They have large positive magnetic susceptibility and form permanent magnets. Examples of ferromagnetic materials are iron, cobalt, and nickel.

Let us now understand some of the important Moving Charges and Magnetism formulas that students must be well aware of:

1. Magnetic Field due to a bar magnet:

IIT JAM exam may ask questions based on the formula for determining the magnetic field created due to a magnetic field. Let us take a look at this:

Axis field: $\mathbf{B} = \frac{\mu_0 \, 2m}{4\pi r^3}$

Equator field: $\mathbf{B} = -\frac{\mu_0 \, m}{4\pi r^3}$

Here:

• B is the magnetic field, which is a vector quantity (measured in Tesla T)
• μ₀ is the permeability of free space/vacuum
• π is the mathematical constant, i.e. 3.1416
• m is the magnetic dipole moment of bar magnet (A·m²)
• r is the distance from the centre of the magnet to the observation point
• r³ indicates how fast the magnetic field weakens with distance
• 2m indicates the factor 2, which accounts for stronger field as compared to equator
• '-' sign indicates that the magnetic field is reversed on the equator

2. Torque on Magnetic Dipole

τ=m×B

Here:

τ = mBsinθ, where θ represents the angle between m (magnetic moment) and B (magnetic field).

Do note that in entrance exams like the NEET exam, questions will not be asked directly on the above formula, but the formula may be used in one part of the question.  Therefore, understanding every formula, the terms used in them and their applications, is very important.

3. Magnetic Potential Energy

$U_m=-\mathbf{m}\cdot \mathbf{B}$ or $U_m$ = $-mB\cos \theta$

4. Gauss's Law for Magnetism:

${\phi }_B=\sum \mathbf{B}\cdot \Delta \mathbf{S}=0$ 

${\phi }_B$is the total magnetic flux passing through a closed surface. Positive flux shows magnetic field lines leaving the surface. Negative flux represents those magnetic field lines that are entering the surface.
∑ is summation over every surface element
B is magnetic flux density vector
ΔS is outward-pointing area vector of the surface patch (m²)
B · ΔS represents the dot product that gives flux through that patch

5. Magnetic Field in a Solenoid

$B_0={\mu }_{0}nI$

Here, 

$B_0$is the axial magnetic-field magnitude within an ideal solenoid. It is measured in Tesla is the permeability of free space. It is equal to $${\mu }_0=4\pi \times {10}^{-7}\text{ T}$$

n indicates turn density or the number of turns per unit of length of the solenoid, i.e. n=N/L

I is the electric current that flows through the windings.

6. Magnetism and Magnetic Intensity

$$\mathbf{M}=\frac{m_{\text{net}}}{V}$$

B = B₀ + Bm 
Bm = μ₀M

$$\mathbf{H}=\frac{\mathbf{B}}{{\mu }_0}-\mathbf{M}$$

B = μ₀(H + M)

Here:

• M indicate the magnetization
• m is the net magnetic dipole moment of sample region
• V is the volume of considered region
• B (vector) indicates the magnetic flux density
• B₀ is the flux density that exists without material
• ${\mathbf{B}}_m$ indicates the contribution to B which is produced by bound (molecular) currents associated with magnetization
• H is the magnetic field intensity 

After learning magnetic field formula class 12, we will move on to learning about bar magnets. The class 12 magnetism and matter chapter starts with a study of the bar magnet and its behaviour in an external magnetic field. Bar magnets are objects with north and south pole, and they have permanent magnetic properties. When iron filings are sprinkled around a bar magnet, they arrange themselves in a pattern that reveals the magnetic field lines. These field lines form continuous closed loops, unlike electric field lines, which begin and end on charges. The magnetic field lines of a bar magnet are similar to those of a current-carrying solenoid, suggesting that a bar magnet can be thought of as a collection of circulating currents.

You can check the following Physics chapter to prepare for the final year examinations:

The pattern of iron filings around a bar magnet allows us to plot the magnetic field lines. Magnetic field lines have several properties that have been discussed in ch 5 physics class 12:

• Magnetic field lines form continuous closed loops.
• The tangent to magnetic field line at any point gives the direction of magnetic field at that point.
• Density of field lines indicates the strength of magnetic field.
• Magnetic field lines do not intersect.

Understanding the similarity between these two becomes important since it can be asked in IISER exam and CUET exam as well. The similarity between the magnetic field lines of a bar magnet and a solenoid indicates that bar magnet is like a large number of circulating currents. Therefore, it is similar to a solenoid. This is further explained by cutting a bar magnet in half results in two smaller magnets, such as cutting a solenoid results in 2 smaller solenoids.

Whenever a magnetic dipole (such as compass needle) is placed in uniform magnetic field, it experiences a torque that aligns it with the field. The potential energy of this magnetic dipole depends on its orientation which is relative to the field. The potential energy is minimized whenever dipole is aligned with the magnetic field and it is maximized whenever it is anti-parallel to the field. The GATE entrance exam may ask questions based on the formula for magnetic potential energy. Therefore, you must know the formula. Mathematically, magnetic potential energy is represented as:

$U_m=-\mathbf{m}\cdot \mathbf{B}$ or $U_m$ = $-mB\cos \theta$