A cross section of Earth’s magnetic field can be represented as a vector field in which the center of Earth is located at the origin and the positive y-axis points in the direction of the magnetic north pole. The equation for this field is

 

where m is the magnetic moment of Earth. Show that this vector field is conservative.

 

F(x, y) = M(x, y)i + N(x, y)j 11. x + y25/2[3yi + (2y? _xj]