Electromagnetic Induction - AP Physics C Electricity and Magnetism

1. Calculate induced EMF: $B = 0.8 \text{T}$, $l = 1 \text{m}$, $v = 5 \text{m/s}$, $\theta = 90^\text{o}$.

   $\text{EMF} = 4 \text{V}$. Motional EMF: $0.8 \times 1 \times 5 \times \sin(90°) = 4$ V.

2. What does a changing magnetic field induce?

   An electromotive force (EMF). Changing magnetic flux creates electric field and drives current.

3. Calculate induced EMF: $B = 0.5 \text{T}$, $A = 2 \text{m}^2$, $dt = 0.1 \text{s}$.

   $\text{EMF} = -10 \text{V}$. $\frac{d\text{Φ}_B}{dt} = \frac{0.5 \times 2}{0.1} = 10$, so EMF = $-10$ V.

4. What does the EMF depend on in an AC generator?

   Speed of rotation and magnetic field strength. Both factors determine the rate of flux change.

5. What is the role of a commutator in a generator?

   Reverses current direction, maintaining output polarity. Mechanical switching device that converts AC to pulsed DC.

6. State the formula for magnetic flux.

   $\text{Φ}_B = B \times A \times \text{cos}(\theta)$. Product of magnetic field, area, and cosine of angle between them.

7. What is Faraday's Law of Electromagnetic Induction?

   $\text{EMF} = -\frac{d\text{Φ}_B}{dt}$. This fundamental law relates EMF to the rate of magnetic flux change.

8. What happens to EMF as magnetic flux increases?

   EMF is induced to oppose the increase. Lenz's law - EMF opposes the flux increase.

9. Identify the primary factor affecting mutual inductance.

   The relative orientation of the coils. Geometric arrangement determines magnetic coupling strength between coils.

10. Find induced EMF if $B = 3 \text{T}$, $l = 0.5 \text{m}$, $v = 2 \text{m/s}$, $\theta = 90^\text{o}$.

    $\text{EMF} = 3 \text{V}$. Motional EMF: $3 \times 0.5 \times 2 \times \sin(90°) = 3$ V.

11. Determine EMF: $N = 100$, $\frac{d\text{Φ}_B}{dt} = 0.02 \text{Wb/s}$.

    $\text{EMF} = -2 \text{V}$. EMF = $-100 \times 0.02 = -2$ V from Faraday's law.

12. How does the number of turns affect induced EMF?

    Induced EMF is proportional to the number of turns. More turns means more flux linkages and greater total EMF.

13. Identify the effect of increased coil turns on a transformer.

    Increased induced voltage. More turns in secondary winding increases output voltage.

14. What reduces energy loss in transformers?

    Using laminated cores. Prevents eddy currents that waste energy as heat.

15. Identify the symbol for magnetic flux.

    $\text{Φ}_B$. Greek phi with subscript B represents magnetic flux quantity.

16. Which rule helps determine the direction of induced current?

    Right-hand rule. Determines direction of induced current from flux change direction.

17. Which direction does the induced current flow?

    Opposes the change in flux (Lenz's Law). Direction determined by energy conservation and opposition principle.

18. State the relationship between EMF and rate of flux change.

    EMF is directly proportional to the rate of change of flux. Faraday's law shows EMF magnitude equals flux rate change.

19. State the formula for energy stored in an inductor.

    $E = \frac{1}{2} L I^2$. Energy stored in magnetic field of inductor.

20. State the formula for induced EMF due to motion.

    $\text{EMF} = B \times l \times v \times \text{sin}(\theta)$. Motional EMF from conductor moving through magnetic field.

21. Calculate the magnetic flux: $B = 1.5 \text{T}$, $A = 3 \text{m}^2$, $\theta = 45^\text{o}$.

    $\text{Φ}_B \text{approx. } 3.18 \text{Wb}$. $1.5 \times 3 \times \cos(45°) = 1.5 \times 3 \times 0.707 ≈ 3.18$ Wb.

22. What happens to the EMF if the magnetic field is constant?

    EMF is zero; no change in flux. No flux change means no induced EMF by Faraday's law.

23. What is self-induction?

    Induction of EMF in the same coil due to changing current. Changing current creates changing magnetic field in same coil.

24. State the formula for induced EMF in a coil.

    $\text{EMF} = -N \frac{d\text{Φ}_B}{dt}$. Faraday's law modified for N turns in a coil.

25. Identify the relationship between flux and induced EMF.

    Induced EMF is proportional to flux change. Faraday's law establishes this direct proportional relationship.

26. Identify the part of a transformer that provides isolation.

    The core. Iron core provides magnetic coupling while electrically isolating windings.

27. What is the primary function of a generator?

    Converts mechanical energy to electrical energy. Uses electromagnetic induction to convert rotational to electrical energy.

28. Find the induced EMF: $B = 2 \text{T}$, $A = 4 \text{m}^2$, $dt = 0.1 \text{s}$.

    $\text{EMF} = -80 \text{V}$. $\frac{d\text{Φ}_B}{dt} = \frac{2 \times 4}{0.1} = 80$, so EMF = $-80$ V.

29. Identify the unit of magnetic flux.

    Weber (Wb). Standard SI unit for magnetic flux, equal to $\text{T} \cdot \text{m}^2$.

30. Find magnetic flux: $B = 0.6 \text{T}$, $A = 2 \text{m}^2$, $\theta = 0^\text{o}$.

    $\text{Φ}_B = 1.2 \text{Wb}$. $0.6 \times 2 \times \cos(0°) = 1.2$ Wb using flux formula.

31. Calculate magnetic flux: $B = 2 \text{T}$, $A = 1 \text{m}^2$, $\theta = 0^\text{o}$.

    $\text{Φ}_B = 2 \text{Wb}$. $2 \times 1 \times \cos(0°) = 2$ Wb using flux formula.

32. Find the energy stored: $L = 2 \text{H}$, $I = 3 \text{A}$.

    $E = 9 \text{J}$. Using $E = \frac{1}{2} \times 2 \times 3^2 = 9$ J.

33. What is the unit of electromotive force (EMF)?

    Volt (V). Standard unit for electrical potential difference and EMF.

34. Identify the factor causing alternating current in a generator.

    Rotation of coil in magnetic field. Rotating coil changes flux continuously, creating sinusoidal EMF.

35. What is the purpose of laminated cores in transformers?

    To reduce eddy currents. Thin insulated sheets reduce circulating currents and energy loss.

36. What is mutual induction?

    Induction of EMF in one coil due to changing current in another. Changing current in one coil affects nearby coil's flux.

37. What changes in a transformer to induce voltage?

    Magnetic flux in the core. Alternating primary current creates changing flux in core.

38. What is the unit of inductance?

    Henry (H). Named after Joseph Henry, measures opposition to current change.

39. What is Lenz's Law?

    Induced EMF opposes the change in magnetic flux. Conservation of energy principle - induced effects oppose their cause.

40. Which law explains the induced current direction?

    Lenz's Law. Lenz's law determines current direction to oppose flux change.

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