As shown in Figure 1 below, a long, straight conducting wire is stretched horizontally directly above a magnetic compass, both of which are separated by distance d. When electrical current is not flowing through the wire, the compass needle points in a direction parallel with the wire’s direction. When a current flows through the wire, the north pole of the needle rotates 60o to the east and comes to rest. Next, as shown in Figure 2, while the current continues to flow, the wire is moved vertically upward to a position distance from the compass. As a result, the north pole of the needle rotates and comes to rest position pointing 45o east of north. What is the value of D/d ?
B = (μo I) / (2πd)
The Attempt at a Solution
The compass in figure 1 has bigger angle because the magnetic field is stronger but I don't know what formula relates the value of magnetic field produced by a very long straight wire to the angle of deflection of compass.