In this example, we use =BAcos to solve for the strength of a magnetic field. A plane surface with area 4.0 cm2 is placed in a uniform magnetic field that is oriented at an angle of 30 to the surface. (a) What is the angle ? (b) If the magnetic flux through this area is 0.90 mWb , what is the magnitude of the magnetic field? For the same B and A , find the angle at which the flux would have one third the value given above (i.e., the angle at which B=3.0104Wb ). Express your answer in degrees.

Review | Constants SOLUTION In this example, we use @ = BA cos o to solve for the SET UP AND SOLVE Part (a): (Figure 1) shows our sketch. As defined earlier, o is the angle strength of a magnetic field. A plane surface with area between the direction of B and a line normal to the surface, so $ = 60 (not 30 0 ). 4.0 cm is placed in a uniform magnetic field that is oriented at an angle of 30 to the surface. (a) What is the Part (b): Because B and o are the same at all points on the surface, we can use angle ? (b) If the magnetic flux through this area is 0.90 DB = BA cos . We solve for B, remembering to convert the area to square meters: mWb , what is the magnitude of the magnetic field? P B B = - 9.0x10-4 Wb A cos o = 4.5 T (4.0x 10-4 m2) (cos 60 ) REFLECT The flux through the surface depends on its angle relative to B. Knowing this angle and the flux per unit area, we can find the magnitude of the magnetic field. Part A - Practice Problem: Figure For the same B and A, find the angle o at which the flux would have one third the value