EMF and Induced Currents

1. EMF and Induced Currents

2. Magnetic Flux • Magnetic flux is defined as the number of field lines passing through an area. • Flux = ф = BA cosθ • It follows that (T)(m2) is a unit for flux. • Note 1 T m2 = 1 Wb • 1 Wb is one Weber

3. Example • A rectangular loop is oriented 42 degrees form a magnetic field as shown at the right. The width of the loop is 0.05 m and the length of the loop is 0.01 m. Determine the strength of the magnetic field, if the flux is 4.8x 10-4 Tm2.

4. Example • B = ф / A cosΘ • B = (4.8x 10-4 Tm2)/ ((0.05m)(0.01 m)(cos 470) • B = 1.4 T

5. Induced EMF, ε • As a conducting wire cuts across the magnetic field lines, an EMF, ε, is induced in the wire. • ε = Blv • The 3rd RHR can be applied to determine the direction of the induced EMF in the wire.

6. Example 2 • An airplane with a 39.9 m wingspan flies northward at 300 m/s. Find the EMF induced between the wingtips. The component of the earth’s magnetic field perpendicular to the wings is 3.0 µT

7. Example 2 • ε = Blv • ε = (3.0 µT)(39.9 m)(300 m/s) • ε = 0.036 V or 36 mV

8. Faraday’s Law • The change of the magnetic flux in a loop will induce an EMF, ε, in the conducting loop. • ε = -N (Δ ф/ Δt) • ε= -N (BA / Δt)

9. Example 3 • A coil of radius 10 cm and 50 turns is oriented perpendicular to a magnetic field. The magnetic field changes from 0. 25 T to zero in a time of 0.20 s. Calculate the induced EMF, ε.

10. Example 3 • ε = N (Δ ф/ Δt) = N (BA / Δt) • ε = 50 (0.25T)(π)(0.10 m)2/ 0.20 s • ε = 2 V