A relatively inexpensive ammeter called a tangent galvanometer can be made using the earth's field. A plane circular coil of N turns and radius R is oriented such that the field Bc it produces in the center of the coil is either east or west. A compass is placed at the center of the coil. When there is no current in the coil, the compass needle points north. When there is a current I, the compass needle points in the direction of the resultant magnetic field B at an angle ? to the north. Show that the current I is related to ? and the horizontal component of the earth's field Be by

= 2 RBa tan e HoN