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Revision: Magnetic Effects of Current and Magnetism >> Magnetic Field and Earth's Magnetism Physics (Theory) ISC (Science) ISC Class 12 CISCE

Definitions [12]

Define Curie temperature.

The temperature above which a ferromagnetic substance becomes paramagnetic is called curie temperature.

Definition: Gyromagnetic Ratio

The ratio of the magnitude of the magnetic dipole moment to the magnitude of the angular momentum of the revolving electron is a constant, independent of the details of the orbit. This ratio is called the ‘gyromagnetic ratio’ for the electron.

Definition: North Pole

When a current-carrying solenoid is suspended by a long thread so that it can move freely in the horizontal plane, then it always rests in the north-south direction. The end of the solenoid pointing north is called the ‘north pole'.

Definition: Bohr Magneton

The minimum value of the magnetic dipole moment of an electron is called the Bohr magneton. 1 Bohr-magneton = 9.27 × 10^-24 A-m².

Definition: Magnetic Lines of Force

The lines of force in a magnetic field are those imaginary lines which continuously represent the direction of the magnetic field. The tangent drawn at any point on a line of force shows the direction of magnetic field at that point.

Definition: Horizontal Component of Earth's Magnetic Field

The horizontal component is the component of the earth’s magnetic field in the horizontal direction in the magnetic meridian.

Definition: Angle of Dip or Magnetic Inclination

The angle of dip at a place is the angle between the direction of earth's magnetic field and the horizontal in the magnetic meridian at that placе.

Definition: Angle of Declination

At any place, the acute angle between the magnetic meridian and the geographical meridian is called the 'angle of declination'.

Definition: South Pole

When a current-carrying solenoid is suspended by a long thread so that it can move freely in the horizontal plane, it comes to rest in the north–south direction. The end of the solenoid other than the one pointing towards the north is called the ‘south pole’.

Definition: Magnetic Equator

The plane perpendicular to the magnetic axis of the earth and passing through the points where the magnetic needle is parallel to the earth's surface intersects the earth’s spherical surface into a circle. This 'circle' is called the 'magnetic equator' of the earth.

Definition: Magnetic Axis

The line joining the magnetic north and the magnetic south poles of the earth is called the 'magnetic axis' of earth.

Definition: Geomagnetic Poles of the Earth

The two places where the needle becomes perpendicular to the Earth’s surface, that is, vertical, are called the geomagnetic poles of the Earth.

Formulae [3]

Formula: Magnetic Field on the Axial Line of a Dipole

B = \[\frac{\mu_{0}}{4\pi}\frac{2m}{r^{3}}\]

Formula: Magnetic Field on Equatorial Line of Dipole

B = \[\frac{\mu_0}{4\pi}\frac{m}{r^3}\]

Formula: Angle of Dip

\[\theta=\tan^{-1}\left(\frac{B_{V}}{B_{H}}\right)\]

Key Points

Key Points: Magnetic Dipole of a Current Loop

A current-carrying loop behaves like a magnetic dipole, similar to a bar magnet.
When placed in a uniform magnetic field, a current loop experiences a torque that tends to align its axis parallel to the field.
By comparing the torque on a current loop with that on an electric dipole, the magnetic dipole moment of a current loop is defined as .
The direction of the magnetic dipole moment is perpendicular to the plane of the loop and is given by the right-hand curled-finger rule.
For a coil having N turns, the magnetic dipole moment is
, and its SI unit is A·m².

Key Points: Magnetic Torque on a Dipole

A bar magnet placed in a uniform magnetic field experiences a torque that tends to align its magnetic axis parallel to the field.
A current loop behaves like a magnetic dipole, and its behaviour in a magnetic field is similar to that of a bar magnet.
According to the modern theory, a magnet consists of many tiny current loops, and the total torque on the magnet is the sum of torques on these loops.
The torque depends on the magnet's orientation in the magnetic field and is maximum when the magnetic axis is perpendicular to the field.
When the magnetic axis is parallel or antiparallel to the magnetic field, the torque becomes zero, and the magnet is in equilibrium.

Key Points: Magnetic Dipole Moment of a Revolving Electron

An electron revolving around the nucleus behaves like a tiny current loop and hence acts as a magnetic dipole.
The magnetic dipole moment of a revolving electron arises due to its orbital motion and is perpendicular to the plane of the orbit.
The direction of magnetic dipole moment is opposite to the direction of the electron’s orbital angular momentum.

Key Points: Properties of Magnetic Lines of Force

Magnetic lines of force emerge from the north pole, enter the south pole, and return to the north pole, forming closed, continuous loops.
No two magnetic lines of force ever intersect, because intersection would imply more than one direction of the magnetic field at a point, which is impossible.
The density of magnetic lines of force represents field strength; lines are closer near the poles, where the field is strong, and farther apart where the field is weak.
In a uniform magnetic field, such as the Earth’s magnetic field at a place, the lines of force are parallel and equally spaced.
Magnetic lines of force do not pass through a neutral point and may enter or leave a magnetic pole at any angle.

Key Points: Equivalence of Solenoid and Bar Magnet

Two current-carrying solenoids show attraction and repulsion; unlike poles attract each other, while like poles repel each other.
The polarity of a solenoid is determined by the end rule: anti clockwise current at an end indicates a north pole, and clockwise current indicates a south pole.
The far axial magnetic field of a finite solenoid is
$\[\frac{\mu_{0}}{4\pi}\frac{2m}{r^{3}}\],$ which is the same as the axial magnetic field of a bar magnet, proving their magnetic equivalence.