Demo Equipment
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Faraday's
- coil, wires, large voltmeter, magnets
Notes: Faraday's law
- Changing flux causes an emf
- The magnitude of the emf is equal to the magnitude of the rate of change of the flux.
Equation
- ℰ = | ΔΦB | / Δt
- Recall, T·m2 = V·s
- → units of ℰ is Volts
- Now, ℰ is not due to a battery.
- Instead, it is due to the interaction between the charges in the conductor and the magnetic field.
Solenoids and coils
- For a solenoid or coil, each loop has a flux.
- Total flux through a solenoid = sum of each loop's flux.
- For a uniform B field, ΦB, total = N ΦB, loop
- ℰ = ΔΦB, total / Δt
Demo: Faraday's law
- I have a large uniform magnet - field strength ~ 0.10 T
- And, a coil with 400 loops, width = 15 cm
- Coil starts out in a region of ~ 0 magnetic field.
- Then, I slide the coil at a speed of 4 cm/s towads the magnets.
Observations
- Voltmeter moves to positive as the coil covers the magnets, then to negative as the coil uncovers the magnets.
- Magnitude of voltage? ~ 0.25 V
Repeat
- Try 2 cm/s (should be ~ 1 V)
- Try 8 cm/s (should be ~ 4 V)
Explanation
- While covering...
- ΦB, total = 400 (0.15 m × x) (0.10 T) = 6 T·m x
- x = 4 cm/s × Δt
- ΦB, total = 0.24 T·m2/s Δt
- ℰ = 0.24 V
- For 2 cm/s, ℰ will be cut in half (0.12 V).
- For 8 cm/s, ℰ will double (0.48 V).
Long Problem: Faraday's law
- There are two solenoids, one inside the other.
- The inner solenoid is 15 cm long, 1.0 cm in radius, and has 250 loops.
- The outer solenoid is also 15 cm long, and has 1200 loops.
- What is the emf in the outer solenoid if the inner solenoid goes from no current to a current of 1.2 A in an interval of 0.50 s?
Solution
- 2: diagram
- 3: L = 0.15 m, r = 0.010 m, Ninner = 250, Nouter = 1200, I = 1.2 A, Δt = 0.50 s
- 4: principles - magnetic field of a solenoid, flux, Faraday's law
- 5: B = μ0 Ninner I / L, ΦB, total = Nouter A B cos(θ), ℰ = ΔΦB, total / Δt
- 6: Compute B due to inner, then change in flux in the outer, then ℰ
- 7: B = 0.0025 T, ΔΦB, total = 0.00095 T·m2, &Esr; = 0.0019 V
- 8: units (B → T, Φ → T·m2, ℰ → V). Solenoid field is < 1 T, which is reasonable.