## Helmholtz Coils –

A two co-axial identical circular magnetic coil that is placed symmetrically along with a common axis and is separated by a distance equal to the radius of the coil. The coil carries equal current in the same direction are called a Helmholtz coil.

This Helmholtz coil is used to producing a reason for the nearly uniform magnetic field. It is also used Din scientific apparatus to cancel the external magnetic field. The resultant magnetic field at the midplane between the coils is equal to the vector sum of the magnetic field produced by the Helmholtz coil individually.

### Force On Charged Particles In A Magnetic Field –

When a charged particle enters into a magnetic field then the charge particle will experience the magnetic force. Let a charged particle of charge q enters into a magnetic field b E with velocity v then magnetic force as on small q will be. The direction of magnetic force f can be found by right hand screw rule.

## Fleming’s Left-Hand Rule –

If first two fingers and a thumb of left hand is stretched such that all the three fingers are are mutually perpendicular. Now the first finger of left hand points towards magnetic field the middle figure points towards velocity v then the stretched thumb will represent the direction of magnetic force.

### Definition Of One Tesla –

The magnetic field b at a point is made to be one tesla if a charge of one coulamb while moving at right angle to the magnetic field with a velocity of one metre per second experiences magnetic force of one Newton.

## Motion Of A Charged Particle In The Uniform Magnetic Field-

Consider a charged particle of charge q moving with velocity v and while moving it enters into a magnetic field b then the magnetic force acting on that charged particle will be e given by multiplication of charge q, velocity, magnetic field and sine of the angle between them.

### Case one –

If a particle enters is perpendicular with the magnetic field then the magnetic force will be. The net magnetic force towards the centre will provide the net centripetal force then the particle will move in the circular path.

**Note –**

Radius of circular part depends on kinetic energy. If velocity is increased then the kinetic energy will also increase. And when velocity increased and kinetic energy increased then the momentum will also be increased. Time period, frequency and angular frequency these are some property is which does not depends on the velocity of the charged particle.

### Case two –

Charge particle enters making an angle theta with the direction of magnetic field. Let a charged particle having charge q enters into a magnetic field with velocity v and when entering it is making an angle then there will be two components of velocity when will be the the in the the direction of magnetic field which is parallel component and other one which is the perpendicular to the direction of magnetic field is perpendicular component. Perpendicular component moves the particle in circular path while parallel component moves the particle and forward linear direction. During this combined motion path of the particle is found to be helical.

### Pitch –

The linear distance covered by the charged particle in the direction of the magnetic field in one revolution of the circular path is known as pitch.

**Note –**

In polar regions there are some dancing projections of different colour which are due to motion of charged particles in the earth magnetic field and this property e is known as call aura.

## Motion Of Charged Particle In A Combined Electric Field and Magnetic Field –

Consider particle q moving with velocity v enters into a region in which electric field and magnetic field both are present then electric force on charge q will be equal to multiplication of charge q and electric field E while the magnetic force on charge q will be equal to multiplication of charge q and VXB. Net force applied on charge q will be equal to q(E+(VXB)). This force is also known as the Lorentz force. Now we consider a simple case in which the electric field and magnetic field are perpendicular to each other then the net force will be equal to q(E-VB)i. If a condition that a particle moves in an electric field and magnetic field in such a way that net force on the charged particle becomes zero and particle remains undeflected then the selection is called velocity selector.

**Note –** This method was employed by JJ Thomson to find the ratio of charge to mass. It is also used to separate charged particles, especially iron according to their charge to mass ratio.