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only for iitians...
how many earth magnetic moment in joule per time inverse
Answers
Answer:
Earth’s Magnetic Field
Magnetic Potential for a dipole field pointing South
V(r) = m • r / (4 π r
3
) = − m cosθ / (4 π r
2
) = scalar magnetic potential of dipole
field. Field is expanded in spherical harmonics. First term (above) is the dipole term.
m = 8 x 1022 Am2
is dipole moment at center of Earth point south
r = distance from dipole
θ = colatitude
B(r) = − µ0 grad V = vector magnetic field
where µ0 = 4π x 10-7 kg m A-2
s
-2 = magnetic permeability in free space (A=amps)
Br = − µ0 dV/dr = − µ0 m 2 cosθ / (4 π r
3
) radial component of magnetic field (up)
Bθ = − µ0 r
-1 dV/dθ = − µ0 m sinθ / (4 π r
3
) tangential component of field (south)
|B| = sqrt( Br
2 + Bθ
2 ) = µ0 m / (4 π R3
) sqrt(sin2
θ +4cos2
θ) = B0 sqrt(1+3cos2
θ)
size of magnetic field at Earths surface
at r = R = 6371*103 m (surface of earth) define:
B0 = µ0 m / (4 π R3
Earth’s Magnetic Field
Magnetic Potential for a dipole field pointing South
V(r) = m • r / (4 π r
3
) = − m cosθ / (4 π r
2
) = scalar magnetic potential of dipole
field. Field is expanded in spherical harmonics. First term (above) is the dipole term.
m = 8 x 1022 Am2
is dipole moment at center of Earth point south
r = distance from dipole
θ = colatitude
B(r) = − µ0 grad V = vector magnetic field
where µ0 = 4π x 10-7 kg m A-2
s
-2 = magnetic permeability in free space (A=amps)
Br = − µ0 dV/dr = − µ0 m 2 cosθ / (4 π r
3
) radial component of magnetic field (up)
Bθ = − µ0 r
-1 dV/dθ = − µ0 m sinθ / (4 π r
3
) tangential component of field (south)
|B| = sqrt( Br
2 + Bθ
2 ) = µ0 m / (4 π R3
) sqrt(sin2
θ +4cos2
θ) = B0 sqrt(1+3cos2
θ)
size of magnetic field at Earths surface
at r = R = 6371*103 m (surface of earth) define:
B0 = µ0 m / (4 π R3
3 * 10-5 Tesla (T) = 3 * 104 nanoTesla
So the strength of the magnetic field at Earth’s surface varies from 30,000nT at the
equator (θ = 90; cos2
θ=0) to 60,000nT at the poles (θ = 0 or 180; cos2
θ=1).
The inclination angle (I) is defined to be the dip of magnetic field: horizontal=0, down is
positive) so:
tan(I) = -Br / | Bθ | = (B0 2 cosθ ) / (B0 sinθ ) = 2/tanθ = 2 tanλ
negative Br because we measure dip pointing down but positive r is up
θ is colatitude; λ = 90 - θ is latitude
Time variation of magnetic field
Secular variation
Intensity
Direction
Westward drift of non-dipole field
Reversals