If the earth's magnetic field has a magnitude `3.4 xx 10^(-5) T` at the magnetic equator of the earth, what would be its value at the earth's goemagnetic poles?

Explanation

Given vac B = 3.4 xx 10^(-5) T `
rArr (mu_(0))/(4 pi) xx ((M)/(R^(3)) = 3.4 xx 10^(-7)`
`M = (3.4 xx 10^(-5) xx R^(3) xx 4 pi)/(4 pi xx 10^(-7))`
` = 3.4 xx 10^(2)R^(3)`
`vacB an poles = (mu_(0))/(4 pi) xx (2m)/(r^(3))`
`= (10^(-7) xx 2 xx 3.4 xx 10^(2)R^(3))/(R^(3))`
` = 6.8 xx 10^(-5)T`