1. A uniform 1.5 T magnetic field passes through the plane of a wire loop with area 0.3 m². What flux passes through the loop when the direction of the 1.5 T field is at a 30 deg angle to the normal of the loop plane?

ans: 0.39 Wb; B*Area*cos(30 deg).

2. A 500 turn circular coil with an area of 0.05 m² is mounted on a rotating frame which turns at a rate of 20 rad/s in the presence of a 0.05 T uniform magnetic field which is perpendicular to the axis of rotation. What is the instantaneous voltage in the coil at the moment that the normal to its plane is at a 90 deg angle to the field?

ans: 25.0 V; at 90 deg, the flux is zero but changing the fastest. In a very small time interval Dt the area "visible" to the field goes from 0 to (area of loop)*omega*Dt, so Dflux/Dt= B*Area*omega = .05T*.05m2*20r/s = 0.05Wb/s. The voltage will be N*Dflux/Dt = 500*0.05.

3. A large jetliner with a wing span of 40 m flies horizontally and due north at a speed of 300 m/s in a region where the magnetic field of the earth is 60 mT directed 50 deg below the horizontal. What is the magnitude of the induced voltage between the ends of the wing?

ans: 550 mV; use V = B*sin(50deg)*l*v.

4. You can calculate the induced current in a ring by setting the voltage from a changing flux V = -DF/Dt equal to the voltage change -LDI/Dt in an inductor. If the magnetic field through a ring of area 1 cm² collapses from 0.02 T to zero and the inductance of the ring is 10^-7 H, what is the induced current in the ring?

ans: 20 A; use Dflux/Dt = L*DI/Dt, cancel Dt, solve for DI = DB*area/L.