Magnetic dipole moment (M) = mL where m is pole strength of the magnet also called magnetic charge magnetic poles are of two types: N- pole and S-pole.
M = ml = lA
Where l is current and A is area. The unit of pole strength is A-m and unit of dipole moment is Am2
Magnetic length / geometric length = 0.84
Torque τ = M x b
F = mB
?BdS = 0 or ∇.B =0
This is gauss law and states that monopole cannot exit. Magnetic field due to a bar magnet along axial line or end - on position.
B = μ0 2 Md / 4π(d2 - l2)2 = 2μ0M / 4πd3 due to a short magnetic dipole (or short magnet)
Magnetic field due to a bar magnet along equatorial line or on broadside on position.
B = μ0 M / 4π (d2 + l2)3/2 (also N to S pole)
= μ0 M /4πd3 (due to a short magnet)
Dimensional formula of B = [ML T-2 A-1]
Unit of magnetic field is tesla (T) or Wb/m2 (SI) or gauss (CGS).
Magnetic potential (V)
B = -dV / dr or V = ∫r∞ - B dr = μ0m / 4πr
Magnetic potential at any point p due to a bar magnate
V = μ0 M cos θ / 4π(r2 - l2 cosθ) = μ0 M cos θ / 4πr2 (due to a short magnet)
Magnetic field strength due to a magnetic dipole (bar magnet at any point p
B = μ0M / 4πr3 1 + 3 cos2 θ
Tan β = sin θ / 2 cos θ = tan θ / 2
Magnetizing field H = B / μo in vacuum dimensional formula is [M0L -1 T o A1]
The electric current enclosed in a closed path of unit length in a magnetic field is defined as magnetizing field
H, that is H = I / L when L = 1 m, H = i
Magnetic flux density or magnetic induction B
B = ∅ / A or B = ∅ if A = 1 m2
That is magnetic lines of force passing through unit normal area in a magnetic field is defined as magnetic induction.
The direction in which a current carrying conductor in a magnetic field experiences no force is th direction of magnetic induction.
Magnetic moment of an electron due to its orbital motion is lμB and due to its spin is μB / 2
M orbital = 1 (eh / 4π ml)
M spin = S (eh / 2ms) = SμB = μB / 2
Where μB is Bohr magneton
μB = eh / 4πm = 0.93 x 10-23 Am2
About 90% of magnetic moment is due to spin motion and only 10% is due to orbital motion.
The magnetic dipole moment of earth is 8 x 1022J/T the magnetic axis makes 11.5 with axis of rotation of earth.
The point where the dipole axis cuts near N-pole and the other near S-pole is termed as the geomagnetic North Pole and the geomagnetic South Pole respectively. Earth's magnetic field changes both in magnitude and direction with passage of time. It is relieved that earth's magnetic field has reversed 171 times in the past 7.6 x 107 years. The latest reversal occurred 10,000 years ago.
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