A tangent galvanometer is an instrument, developed in the nineteenth century, designed to measure current based on the deflection of a compass needle. A coil of wire in a vertical plane is aligned in the magnetic north-south direction. A compass is placed in a horizontal plane at the center of the coil. When no current flows, the compass needle points directly toward the north side of the coil. When a current is sent through the coil, the compass needle rotates through an angle θ. Derive an equation for θ in terms of the number of coil turns N, the coil radius r, the coil current I, and the horizontal component of Earth's field BH.