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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

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

Sun Dec 25, 2022

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