Induced Currents and Magnetic Forces - AP Physics C Electricity and Magnetism

1. What influences the magnitude of induced EMF?

   Rate of change of magnetic flux. Faster flux changes produce larger induced EMF.

2. What does the magnetic force on a loop depend on?

   Current, magnetic field strength, loop area, angle. Force depends on current, field strength, geometry, and orientation.

3. What is the relationship between induced EMF and loop resistance?

   Induced current is inversely proportional to resistance. Current equals EMF divided by resistance (Ohm's law).

4. Calculate torque: $n = 2$, $I = 1 \text{ A}$, $A = 0.1 \text{ m}^2$, $B = 0.5 \text{ T}$, $\theta = 90^\text{o}$.

   $\tau = 0.1 \text{ Nm}$. $\tau = 2 \times 1 \times 0.1 \times 0.5 \times \sin(90°) = 0.1$ Nm.

5. State the unit of magnetic moment.

   Ampere-square meter (A·m²). Product of current and enclosed area for magnetic dipole.

6. What is the formula for induced EMF in a loop?

   $\text{EMF} = -\frac{d\text{Φ}_B}{dt}$. Faraday's law for single loop electromagnetic induction.

7. What happens to the induced EMF if the loop area increases?

   Induced EMF increases. Larger area means more magnetic field lines enclosed.

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

   No induced EMF. No flux change means no EMF by Faraday's law.

9. What is the formula for the torque on a current loop?

   $\tau = \text{n} \times \text{I} \times \text{A} \times \text{B} \times \text{sin}(\theta)$. $n$ is number of turns, $A$ is loop area.

10. Calculate Lorentz force: $q = 1 \text{ C}$, $E = 5 \text{ N/C}$, $v = 2 \text{ m/s}$, $B = 3 \text{ T}$, $\theta = 90^\text{o}$.

    $\text{F} = 11 \text{ N}$. $F = qE + qvB = 1(5) + 1(2)(3) = 11$ N.

11. What does a galvanometer measure?

    Electric current. Detects small currents through magnetic deflection.

12. Identify the effect of increasing the magnetic field strength on induced EMF.

    Increases induced EMF. Stronger field creates larger flux changes per time.

13. What is the direction of force on a charge moving parallel to a magnetic field?

    No magnetic force. Force is zero when velocity parallel to field.

14. Define magnetic force on a current-carrying wire.

    $\text{F} = \text{I} \times \text{L} \times \text{B} \times \text{sin}(\theta)$. Current-carrying wire experiences force in magnetic field.

15. What is Faraday's law of electromagnetic induction?

    $\text{EMF} = -\frac{d\Phi_B}{dt}$. Negative sign indicates Lenz's law - opposing flux changes.

16. Calculate magnetic force: $I = 3 \text{ A}$, $L = 2 \text{ m}$, $B = 1 \text{ T}$, $\theta = 90^\text{o}$.

    $\text{F} = 6 \text{ N}$. $F = ILB\sin(90°) = 3 \times 2 \times 1 = 6$ N.

17. Identify the formula for the Lorentz force.

    $\text{F} = \text{q}(\text{E} + \text{v} \times \text{B})$. Combined electric and magnetic forces on charged particle.

18. What is the principle of electromagnetic induction?

    Inducing EMF through changing magnetic flux. Faraday's fundamental discovery linking magnetism and electricity.

19. What is the formula for magnetic flux?

    $\text{Φ}_B = \text{B} \times \text{A} \times \text{cos}(\theta)$. $\theta$ is angle between $\vec{B}$ and area normal.

20. What does a change in magnetic flux produce?

    Induced EMF. Faraday's law links flux change to EMF generation.

21. Identify the unit of magnetic flux.

    Weber (Wb). Same as Tesla-meter squared ($\text{T}\cdot\text{m}^2$).

22. What is the right-hand rule used for?

    Determining direction of magnetic force or field. Fingers point along first vector, thumb shows result direction.

23. What is the unit of magnetic field strength?

    Tesla (T). Also written as Weber per square meter (Wb/m²).

24. Find the force on a charge: $q = 1 \text{ C}$, $v = 2 \text{ m/s}$, $B = 3 \text{ T}$, $\theta = 90^\text{o}$.

    $\text{F} = 6 \text{ N}$. $F = qvB\sin(90°) = 1 \times 2 \times 3 = 6$ N.

25. Define motional EMF.

    EMF induced in a conductor moving in a magnetic field. Moving conductor cuts magnetic field lines inducing EMF.

26. What is the role of a transformer?

    Changes voltage levels in AC circuits. Uses electromagnetic induction to step voltage up or down.

27. What is the formula for motional EMF?

    $\text{EMF} = \text{B} \times \text{L} \times \text{v} \times \text{sin}(\theta)$. $\theta$ is angle between velocity and magnetic field.

28. State Ampère's circuital law.

    $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$. Magnetic field circulation equals permeability times enclosed current.

29. What is the SI unit for electric current?

    Ampere (A). Base unit for electric current in SI system.

30. State the formula for the magnetic field of a solenoid.

    $\text{B} = \frac{\text{μ}_0 \text{n} \text{I}}{\text{L}}$. $n$ is turns per unit length, creates uniform field inside.

31. Which factor determines the direction of induced current?

    Lenz's Law. Induced current opposes the flux change causing it.

32. Identify the direction of the magnetic force on a positive charge moving perpendicularly to the field.

    Perpendicular to both velocity and field. Right-hand rule determines force direction from cross product.

33. State the relationship between magnetic field and force on a moving charge.

    $\text{F} = \text{q}(\text{v} \times \text{B})$. Cross product gives force perpendicular to both $\vec{v}$ and $\vec{B}$.

34. What is the effect of decreasing loop resistance on induced current?

    Induced current increases. Lower resistance allows more current for same EMF.

35. What is the role of a commutator in a DC motor?

    Reverses current direction to maintain rotation. Switches connections to maintain consistent torque direction.

36. Calculate the motional EMF: $B = 2 \text{ T}$, $L = 0.5 \text{ m}$, $v = 3 \text{ m/s}$, $\theta = 90^\text{o}$.

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

37. State Lenz's Law.

    The induced EMF opposes the change in magnetic flux. Conservation of energy principle preventing perpetual motion.

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