An engineer tests a new magnetic flux sensor consisting of a two-dimensional square membrane, 4.10 cm on each side. The sensor measures the magnetic flux through the membrane. The engineer places the sensor so that it is parallel to and 2.10 cm above the xy-plane in the field region. The edges of the sensor are aligned to the positive x- and y-axes. The normal vector for the sensor's surface points straight up, parallel to the z-axis. 15 n X To test the new sensor, the engineer sets up a region of magnetic field. The magnetic vector field is described by B = (0.0200 T-cm³) x²yî + (0.0700 T-cm2) xyĵ- (0.267 T-cm¯³) xy² k What magnetic flux PB does the sensor measure?

An engineer tests a new magnetic flux sensor consisting of a two-dimensional square membrane, 4.10 cm on each side. The sensor measures the magnetic flux through the membrane. The engineer places the sensor so that it is parallel to and 2.10 cm above the xy-plane in the field region. The edges of the sensor are aligned to the positive x- and y-axes. The normal vector for the sensor's surface points straight up, parallel to the z-axis. 15 n X To test the new sensor, the engineer sets up a region of magnetic field. The magnetic vector field is described by B = (0.0200 T-cm³) x²yî + (0.0700 T-cm2) xyĵ- (0.267 T-cm¯³) xy² k What magnetic flux PB does the sensor measure?