If a charged particle having charge q mass m enters a magnetic field B with a velocity v then the force experienced by the particle is
F = q (v x B)
This principle is used in television receiver for deflection of electrons. The unit of magnetic field is
B = Wb/m -2 or teals
The CGS unit is gauss = Maxwell/cm2
If electric and magnetic fields are present then the force experienced is called Lorentz force and is given by
F = q E + q (v x B0)
J.J. Thomson used this method to fined e/m
If the velocity of a charged particle is always perpendicular to the magnetic field then it describes a circle of radius R such that
R = mv/qB
Time period of revolution
T = 2π/v = 2πm/qB
F = I/T = qB/2 πm
If the charged particle enters obliquely in a magnetic field then the velocity can be resolved into x and y components the y perpendicular component describes a circle and x parallel component describes linear motion. Therefore, the particle moves in a helix.
The horizontal or linear distance moved in one complete revolution is called the pitch of the helix.
Pitch of the helix = vxT = vx (2πm/qB)
Magnetic force of due to a current carrying conductor
d F = I dI x B
the direction of force is determined using Fleming's left hand rule.
If the conductor is straight F = 1 I x B
Otherwise integrate to find F = ∫1 dI x B
Torque acting on a current carrying loop τ = I A x B
If there are n loops τ = nI A x B where A is area vector A = Ib
τ = M x B' where M = IA or nIA is magnetic dipole moment.
Biot savart law
dB = μ0/4π I dI x r/r3
is the magnetic field due to a length dl of a conductor carrying current I at a distance r from the conductor.
dB = π0 IdI din ∅ / 4 π2 where μ0 = 4π x 10 - 7 Wb (A-m) -1 or henerym-1
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