Magnetic Effects of Current
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 straight wire
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
Motion of a charged particle in a uniform magnetic field
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
Magnetic force on a current carrying conductor (Lorentz Force)
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
Force between two parallel current carrying conductors
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