The earth's magnetic field at geomagnetic poles has a magnitude `8xx10^(-5)T`. Find the magnitude and the direction of the field at a point on the earth's surface where the radius makes an angle of `120^(@)` with its axis of the earth's assumed magnetic dipole. What is the inclination dip at this point?

Explanation

The geomagnetic poles are in end on position.
The magneic field at geomagnetic poles
`" " B'=(mu_(0))/(4pi).(2M)/(R^(2)),B'=8xx10^(-5)T`
The magnetic field at point P
`" " B'=(mu_(0)M)/(4piR^(3))(1+3cos^(2)theta)^(1//2)`
`" " (B')/(2)(1+3 cos^(2)theta)^(1//2)`
`" " (8xx10^(-5^(2)))/(2)[1+3cos^(2) 120^(@)]^(1//2)`
`" " =4xx10^(-5)[1+(3)/(4)]^((1)/(2)`
`" " tan alpha=(1)/(2) tan theta=(1)/(2) tan120^(@)`
`" " alpha= tan^(-1)((-sqrt3)/(2))`
Dip `theta` is an angle made by the earth's magnetic field with the horizontal plane
`" " phi=alpha-90^(@)=tan^(-1)((-sqrt3)/(2))-90^(@)`