# Magnetism

Magnetic Field

A magnetic field is a region of space around a magnet where magnetic forces act. It is represented by magnetic field lines, which are imaginary lines that indicate the direction of the magnetic force at any point in space. The closer the field lines are together, the stronger the magnetic field.

Magnetic Dipole

A magnetic dipole is a pair of magnetic poles of equal strength and opposite polarity. The magnetic moment of a magnetic dipole is a measure of its strength.

Force on a Magnetic Dipole in a Magnetic Field

The force on a magnetic dipole in a magnetic field is given by:

``````F = MB sin θ
``````

where:

• F is the force
• M is the magnetic moment of the dipole
• B is the magnetic field strength
• θ is the angle between the magnetic moment and the magnetic field

Torque on a Magnetic Dipole in a Magnetic Field

The torque on a magnetic dipole in a magnetic field is given by:

``````τ = MB sin θ
``````

where:

• τ is the torque
• M is the magnetic moment of the dipole
• B is the magnetic field strength
• θ is the angle between the magnetic moment and the magnetic field

Motion of a Charged Particle in a Magnetic Field

A charged particle moving in a magnetic field experiences a force perpendicular to its velocity and to the magnetic field. The magnitude of the force is given by:

``````F = qvB sin θ
``````

where:

• F is the force
• q is the charge of the particle
• v is the velocity of the particle
• B is the magnetic field strength
• θ is the angle between the velocity and the magnetic field

Magnetic Materials

Materials can be classified into three types based on their magnetic properties:

• Ferromagnetic materials, such as iron, nickel, and cobalt, are strongly attracted to magnets. They can be magnetized and retain their magnetism even after the external magnetic field is removed.
• Paramagnetic materials, such as aluminum and magnesium, are weakly attracted to magnets. They can be magnetized, but they lose their magnetism when the external magnetic field is removed.
• Diamagnetic materials, such as copper and gold, are weakly repelled by magnets. They cannot be magnetized.

Applications of Magnetism

Magnets have many important applications in everyday life. Some examples include:

• Compasses: Compasses use a magnetized needle to align itself with the Earth's magnetic field, which always points north.
• Electric motors: Electric motors use magnetic fields to create a force that rotates a shaft.
• Magnetic resonance imaging (MRI): MRI machines use magnetic fields to create images of the inside of the body.
• Magnetic storage devices: Magnetic storage devices, such as hard drives and floppy disks, use magnetic fields to store data.

Magnetization:

The magnetization M of a given sample material can be defined as the net magnetic moment of that material per unit volume. Mathematically,

Let us now consider the case of a solenoid. We take a solenoid with n turns per unit length and the current through which is given by I, then the field inside the solenoid can be given as:

If we now fill the inside of the solenoid with a non-zero magnetized material, the field inside the solenoid should be greater than before. The net magnetic field B inside the solenoid can be given by

Where Bm gives the field generated by the nuclear material. Here, Bm is proportional to the magnetization of the material, M. Mathematically

Here µ0 is the vacuum permeability constant. Now let's talk about another concept: the magnetic intensity of a material. The magnetic intensity of a material can be given as follows

From this equation, we see that the total magnetic field can also be defined as follows

Here the field due to external factors (e.g. the current in the solenoid) is given as H and the field due to the nature of the core as M. The latter quantity i.e. M depends on the external effects and is given by

Where χ is the magnetic susceptibility of the material. It measures the response of the material to an external field. The magnetic susceptibility of a material is small and positive for paramagnetic materials and small and negative for diamagnetic materials.

Here, the expression µr is called the relative magnetic permeability of the material, which is analogous to the dielectric constants of electrostatic electricity. We define magnetic permeability.

Properties of magnetic field lines:-

Some important features of magnetic field lines are listed below –

• The tangent of the lines of force of the magnetic field gives the direction of the magnetic field.
• ·   The proximity or density of the field lines is directly proportional to the strength of the field.
• ·   The magnetic field lines appear to rise or begin at the North Pole and merge or end at the South Pole. Inside a magnet, the direction of the magnetic field lines is from the South Pole to the North Pole.
• ·    Magnetic field lines never cross.
• ·  The magnetic field lines form a closed loop. Field lines have both direction and magnitude at any point in the field. Therefore, the magnetic field lines are represented by a vector.  They indicate the direction of the magnetic field.
• ·    The magnetic field is stronger at the poles because the  lines of force are denser near the poles.