## Introduction :

- The magnetic effects of electric current were first discovered by Oersted.
- An electric charge in motion sets up a magnetic field around it.
- An electric charge moving in an external magnetic field experiences a force.
- A stationary electric charge produces only electric field. But a moving electric charge produces electric field and magnetic field.

Magnetic field due to straight conductor carrying current :

- The magnetic field is circular.
- The magnetic lines of force are concentric circles with centers lying on axis of the conductor.
- The plane of circle is perpendicular to direction of the current.
- If the current flows through the conductor in upward direction, magnetic lines of force are formed in anti clock wise direction.
- If the current flows through the conductor in downward direction, magnetic lines of force are formed in clock wise direction.

The direction of the magnetic field with respect to the current can be found by the Ampere right hand rule or Maxwell's cork screw rule.

Ampere right hand rule :

- For linear currents: If the wire is grasped in the palm of the right hand with the stretched thumb pointing in the direction of current, the fingers curl in the direction of magnetic field. (i.e., the magnetic lines of force.)
- For circular currents: If the direction of current coincides with the direction of the curl of the fingers of the right hand, the stretched thumb points in the direction of magnetic field at center of the loop.

Maxwell's cork screw rule:

If we imagine a right hand cork screw to be driven along the direction of the current in the conductor, the direction in which the thumb rotates represents the direction of the magnetic field.

- The magnitude of the field produced by an electric current can be determined by using the Biot-Savart law or Ampere's law.

Biot-Savart law :

The magnetic induction dB at a point P due to an infinitesimally small element of current (length dl and current I) at a distance 'r' is given by

The magnetic induction B due to straight wire of finite length carrying current "I" at a distance "d" is given by

- If the wire is infinitely long, then

- Magnetic induction on the axis of a circular current carrying coil is given by,

a) The direction of B ⃗ is as shown in the figure. For current in anti clock wise direction, B ⃗ is out of the page, along the axis of coil.

b) If the fingers of right hand are curled along the direction of flow of current, the thumb points in the direction of B ⃗.

c) Magnetic field at center of coil is given by,

b) If the fingers of right hand are curled along the direction of flow of current, the thumb points in the direction of B ⃗.

c) Magnetic field at center of coil is given by,

d) Magnetic field at a point on the axis of the coil, when x>>R, then

Thus a current carrying coil of area of cross section A and number of turns N, carrying a current I can be regarded as magnetic dipole of magnetic moment NIA.

Magnetic force on a charged particle :

If a charge particle of positive charge q travels with a velocity 'v' making and angle θ with the direction of the magnetic field of induction B, the particles experiences a force,

Fleming's left hand rule :

Stretch the fore finger, central finger and the thumb of the left hand mutually perpendicular to each other. If the fore finger represents the direction of magnetic field and the central finger represents the current then the thumb gives the direction of force on the conductor.

This rule applies only for positive charges. If it is a negative charge, say an electron, its direction of motion should be reversed to apply Fleming left hand rule.

2. The path of the particle will be a straight line i.e., particle will keep on moving on the same path.

3. The values of momentum (p) and kinetic energy remains constant.

2. The direction of F(m) will be normal to the velocity of particle.

3. The path of the particle will be circular.

This rule applies only for positive charges. If it is a negative charge, say an electron, its direction of motion should be reversed to apply Fleming left hand rule.

- When the charged particle is moving parallel to the magnetic field, then

2. The path of the particle will be a straight line i.e., particle will keep on moving on the same path.

3. The values of momentum (p) and kinetic energy remains constant.

- When the charged particle is moving at right angles to the magnetic fields, then

2. The direction of F(m) will be normal to the velocity of particle.

3. The path of the particle will be circular.

The magnetic force acting on the particle provides it necessary centripetal force for its circular motion

Time period of charged particle is

- When the particle enters the magnetic field at an angle θ of with B, The path of the particle will be helical.

Pitch of the path :

The linear distance covered by the particle in one time period in the direction of magnetic field is defined as pitch.

- When the charge particle enters crossed electric and magnetic fields:

The velocity of such a particle is given by

The momentum of the particle p=qBr

1. Magnetic force on a current carrying conductor:

If a current carrying conductor of length l is placed making an angle with the direction of magnetic field of induction B, the force exerted by the magnetic field on the conductor is

Note :

2. Force between two parallel conductors carrying current:

If the current is in opposite direction there is a force of repulsion.

An equal force is exerted by the second conductor on the first. The force of attraction or repulsion per unit length of the conductor is

Note:

Torque on a current loop :

A rectangular coil of area 'A' containing n turns and carrying a current i is placed in a uniform magnetic field of induction B.

If θ is the angle between normal to the plane of coil and magnetic field then torque on coil is

If θ is the angle between normal to the plane of coil and magnetic field then torque on coil is

If α is the angle between the plane of the coil and magnetic field then Torque on coil is given by