Van Allen Belt


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Estimating Energy Stored in the Geomagnetic Field

The magnetic field of the earth is complicated, not a simple dipole, but it can be approximated that way.

B_r = - 2 B_0 left( { { R_E } \over r } right)^3 \cos \theta

B_{\theta} = - B_0 left( { { R_E } \over r } right)^3 \sin \theta

dE = { { {B_r}^2 + {B_{\theta}}^2 } \over { 2 {\mu}_0 } } ~ dV

dV = 2 \pi r \sin \theta dR d\theta

dE = { { {2 B_0 left( { { R_E } \over r } right)^3 \cos \theta}^2 + {B_0 left( { { R_E } \over r } right)^3 \sin \theta}^2 } \over { 2 {\mu}_0 } } ~ 2 \pi r \sin \theta dR d\theta

dE = { 2 \pi {B_0}^2 { R_E } \ over { { 2 {\mu}_0 } r^5 } } ( 3 ( \cos \theta )^2 + 1 ) \sin \theta dR d\theta