A charge q moving in a region where there is an electric field as well as a magnetic field experiences a force, given by

N

Magnetic field induction due to a current element

**Unit:** T (tesla)

**(a)** Magnetic induction at the center of a circular coil of radius R carrying a current I is

, where N is the number of turns in the coil

**(b)** Magnetic induction at the centre due to circular arc conductor carrying current I

**(c)** Magnetic induction about a long straight conductor at a distance r from its center

**(d)** Magnetic induction at a distance r due to a finite length of conductor

**(e)** Magnetic induction along the axis of a circular coil carrying current I

where N is the number of turns, R is the radius and x is the distance of point from the center of the coil.

The force F on a straight conductor carrying a current placed in a magnetic field of induction, B is

where θ is the angle between dI and B

**(a)** A straight conductor of length L_{1} placed at right angle to B experiences a force,

newtons

**(b)** The magnetic field is due to a parallel conductor L_{2} carrying a current I_{2} placed at a distance r from the first conductor,

The force on

The force is attractive if the currents are in the same direction, and repulsive if they are in opposite directions

**(a) Bar magnet**

The mutual interaction force between two small magnets of magnetic moment M_{1} and M_{2} is

**(b) Current loop**

A current loop of area of cross-section A, and number of turns N, carrying a current I is equivalent to a magnetic dipole of magnetic moment μ_{m} where

**(i)** μ_{m} = NIA

**(ii)** magnetic potential energy

**(iii)** mangnetic force,

If a charged particle is projected with velocity v at an angle θ with the magnetic field B, then it follows a helical path of radius r, its time period is T and the pitch of the helix is p

**(a)**

**(b)**

**(c)** , p is the pitch of helix.

where c is the torisional couple per unit twist, N is the number of turns in the coil and A is the area of cross-section of the coil, and θ is the deflection in radians.

**(a) Magnetization vector **

**(b) Magnetic field intensity**

, where is called magnetic susceptibility

∴, called relative permeability

where μm is permeability of the medium

Thus,

**(c) Curie’s Law**

As the temperature increases the susceptibility of paramagnetic substances decreases

or where C is Curie’s constant

Ferromagnetic materials when heated become paramagnetic beyond Curie temperature. Thus for ferromagnetic substances

where T_{C} is Curie temperature

**(d) Comparison among paramagnetic, Diamagnetic and Ferromagnetic materials**

**(e) Hysteresis**

When applied magnetising field is removed the magnetism B or I that remains in the material is called retentivity. In figure, OX = OU = retentivity.

The magnetizing force or H applied in negative –direction to make retentivity zero is called coercivity. In figure OY = OV = coercivity

Vertical component of earth’s magnetic field

Horizontal component of earth’s magnetic field,

where = Resultant magnetic field

θ = angle of dip

φ = angle of declination

At magnetic equator, θ = 90^{0}

At magnetic pole, θ = 90^{0}