Magnetic field on t:quatur of Earth is `4 xx 10^(-5)` T. Radius of Earth is 6400 km, then magnetic dipole moment of Earth is about ...... `Am^(-2)`.

Options

A. `10^(23)`
B. `10^(20)`
C. `10^(16)`
D. `10^(10)`

Answer

A

Explanation

Magnetic field at equator of Earth,
`B_(E) = (mu_0 m)/( 4pi R^3)`
`therefore m= (4pi B_(E) R^(3) )/( mu_0)`
`therefore m= (4 xx 10^(-5) xx (6.4 xx 10^(6) )^(3) )/(10^(-7) ) [ because (mu_0)/( 4pi ) = 10^(-7)]`
`therefore m= 1048 . 576 xx 10^(20) `
`therefore m ~~ 1.0xx 10^(23) " "therefore m~~ 10^(23) "Am"^(2)`