Magnetic field--

In 1820 O rested observed that a compass needle shows deflection when brought near a current carrying wire this means electric current gives rise to magnetism

Bio t Savart Law --

This law gives magnitude of magnetic field at any point due to current carrying conductor

according to this law magnetic field dB at any point P due to current element idl is

dB = μ0 /4π . idl sin¢/r²

Where μ0 is absolute permeability of air

μ= 4π×(10)-⁷

Magnetic field due to current carrying wire of finite length at a point p situated at a normal distance r is given by

B= μ0 I/4πr. (sina+sin b)

If a=b= 90°then

B = μ0 I/2πr

Particle carrying a positive charge q moving with a velocity vector v enters a magnetic field B it experiences a force which is given by the expression

F = qv B sin ¢

The force F is always perpendicular to the both velocity and the magnetic field trajectory of a charged particle depends upon the angle between velocity and the magnetic field

--- angle between them is zero degree that is they are parallel to each other v||B then

F= qv B = 0

-- angle between velocity of the particle and the magnetic field is 90 degree that is they are perpendicular to each other then force is maximum sin 90 =1

F= qv B

When force is maximum at provide centripetal force and the path of the particle is a circle so

the angular velocity of the particle is

Centripetal force = mv²/r= qv B

v/r= B q/m= w

Time period of rotation is 2π/w

T= 2π/w= B q/2πm

If a current carrying conductor length l is placed in a magnetic field B such that it makes an angle with the direction of the field it experiences a force called Lorentz force and is given by

F = Bil sin¢

If if angle a zero degree then force = 0

angle is 90 degree then force is maximum

that F=Bil

When two long straight conductor carrying currents i1 and i2 are placed parallel at a distance of a from each other then a mutual force of attraction acts between them

F= μ/4π. 2I1I1l/a

Where l is the length of that portion of the conductor on which force is to be calculated

Show the force per unit length is

F/l= μ/4π. 2I1I1/a