Magnetic Fields - AP Physics 2

1. State the formula for the magnetic field inside a toroid.

   $B = \frac{\mu_0 n I}{2\pi r}$. Toroidal geometry confines field within the torus structure.

2. State the formula for the magnetic field inside a solenoid.

   $B = \mu_0 n I$. Field is uniform inside; $n$ is turns per unit length.

3. What is the definition of a Tesla?

   1 Tesla = 1 N/(A·m). Force per unit current per unit length in magnetic field.

4. State the expression for the force on a moving charge in an electric and magnetic field.

   $F = q(E + v \times B)$. Complete Lorentz force including both electric and magnetic components.

5. What is the Lorentz force equation?

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

6. Identify the main factor that affects the magnitude of the magnetic force on a conductor.

   Current (I). Force is directly proportional to current flowing through conductor.

7. State the unit of magnetic field strength in the SI system.

   Tesla (T). Named after Nikola Tesla; equivalent to $\text{Wb/m}^2$.

8. State the formula for the magnetic field at a point on the axis of a current loop.

   $B = \frac{\mu_0 I R^2}{2(x^2 + R^2)^{3/2}}$. Field strength decreases rapidly with distance from loop center.

9. What is the principle behind the operation of a galvanometer?

   Torque on a current loop in a magnetic field. Current loop rotates in magnetic field producing measurable deflection.

10. Find the magnetic field strength inside a solenoid with $n = 1000 \, \text{turns/m}$ and $I = 0.01 \, \text{A}$.

    $1.26 \times 10^{-5} \text{ T}$. Using $B = \mu_0 n I$ with given turn density and current.

11. Choose the correct expression for the force between two parallel conductors carrying current.

    $F/L = \frac{\mu_0 I_1 I_2}{2\pi d}$. Force per unit length between parallel current-carrying conductors.

12. What is the relationship between magnetic moment and torque?

    $\tau = \mu \times B$. Torque is cross product of magnetic moment and field vectors.

13. State the formula for the magnetic field at the center of a circular loop of wire.

    $B = \frac{\mu_0 I}{2R}$. Field at center is half that of infinite solenoid.

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

    $\tau = nIAB \sin \theta$. Torque depends on loop area $A$ and angle $\theta$ with field.

15. What is the formula for the energy stored in a magnetic field?

    $U = \frac{1}{2}LI^2$. Energy stored depends on inductance $L$ and current squared.

16. What is the formula for the Hall voltage in a conductor?

    $V_H = \frac{IB}{net}$. Hall effect: voltage across conductor in magnetic field.

17. Calculate the magnetic field strength 1 m away from a 5 A current-carrying wire.

    $1 \times 10^{-6} \text{ T}$. Using $B = \frac{\mu_0 I}{2\pi r}$ with given values.

18. Identify the variable that denotes the number of turns per unit length in a solenoid.

    $n$. Turn density determines magnetic field strength in solenoid.

19. Identify the rule used to determine the direction of the magnetic force on a moving charge.

    Right-hand rule. Point fingers along $v$, curl toward $B$, thumb shows force direction.

20. What is the formula for the magnetic field due to a long, straight current-carrying wire?

    $B = \frac{\mu_0 I}{2\pi r}$. Field decreases as $1/r$ with distance from wire.

21. What is the principle behind magnetic levitation?

    Repulsion of like magnetic poles. Like poles repel, creating upward force against gravity.

22. What is the formula for the magnetic force on a current-carrying wire?

    $F = I(L \times B)$. Current $I$ and length $L$ replace charge and velocity in force equation.

23. What is the value of the permeability of free space ($\mu_0$)?

    $4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}$. Fundamental constant relating magnetic field to current.

24. What is the unit of magnetic flux?

    Weber (Wb). Named after Wilhelm Weber; measures magnetic field through area.

25. Identify the relationship between magnetic flux and magnetic field.

    $\Phi_B = B \cdot A \cdot \cos \theta$. Flux depends on field strength, area, and orientation angle.

26. Which device uses magnetic fields to separate charged particles by mass?

    Mass spectrometer. Different masses follow different curved paths in magnetic field.

27. Which option correctly describes the Biot-Savart Law?

    It relates magnetic fields to the currents which produce them. Fundamental law connecting magnetic fields to their current sources.

28. Find the magnetic force on a 2 C charge moving at 3 m/s perpendicular to a 4 T magnetic field.

    24 N. Using $F = qvB$ with perpendicular motion: $2 \times 3 \times 4 = 24$.

29. Identify the force direction if a proton moves south in a magnetic field pointing upwards.

    West. Using right-hand rule: velocity south, field up gives force west.

30. Determine the magnetic force on a wire if $I = 3 \, A$, $L = 2 \, m$, and $B = 0.5 \, T$.

    3 N. Using $F = ILB$ for perpendicular orientation: $3 \times 2 \times 0.5$.

31. What is the formula for the magnetic force on a moving charge?

    $F = q(v \times B)$. Cross product shows force is perpendicular to both $v$ and $B$.

32. Find the direction of force on an electron moving north in a magnetic field directed east.

    Downward. Electron has negative charge; force opposes right-hand rule direction.

33. What is the direction of the magnetic force on a positive charge moving in a magnetic field?

    Perpendicular to both velocity and magnetic field. Cross product in Lorentz force creates perpendicular direction.

34. What is the expression for the magnetic field of a moving charge?

    $B = \frac{\mu_0}{4\pi} \frac{q(v \times r)}{r^3}$. Biot-Savart law for field produced by moving point charge.

35. What is the formula for the cyclotron frequency of a charged particle?

    $f = \frac{qB}{2\pi m}$. Frequency of circular motion in uniform magnetic field.

36. What is the definition of magnetic flux density?

    Magnetic flux per unit area. Magnetic field $B$ represents flux density through a surface.

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