In order to impatt an angular velocity to an earth satellite the geomagnetic field can be used.Find the maximum possible angular velocity about its own axis gained by the satellite if a storage battery with a capacity of `Q=5 Amp`.hours is discharged suddenly through a coil of `N=20` turns wound around the satellite's surface along the circumference of the largest circle.The satellite has a mass of `m=10^(3) kg` and is a thin walled uniform sphere.The geomagnetic field is parallel to the winding plane and its flux density is `B=0.5 Gauss`.`(1 Gauss =10^(-4)Tesla)`

Answer

`omega=3/2(BNpiQ)/M=2.7pixx10^(-2) rad//s`.

Explanation

Torque on the (coil+sphere) due to flow of charge through coil is `=|vecp xx vecB|`(where `p` is the dipole moment of the coil and `vecB` is the geomagnetic field)
`=iNpir^(2)B=I(domega)/(dt)`
`therefore domega=(Npir^(2)B)/l"idt"` or `omega=(Npir^(2)B)/(2/3mr^(2))underset(0)overset(Deltat)int "idt" =(3N r B Q)/(2M)`