Magnetism and Moving Charges - AP Physics C Electricity and Magnetism

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

   $B = \frac{\mu_0 N I}{2 \pi r}$. Field inside toroidal coil depends on total turns and radius.

2. Calculate the cyclotron radius for a proton, $B = 0.2$ T, $v = 2 \times 10^6$ m/s.

   $r = 0.1 \, \text{m}$. Using $r = \frac{mv}{qB}$ with proton mass and given parameters.

3. State the formula for the magnetic force on a current-carrying wire.

   $F = ILB \sin \theta$. Force on wire depends on current, length, field strength, and orientation angle.

4. What causes the magnetic force between two parallel wires?

   Interaction of magnetic fields created by the currents. Each wire creates field that exerts force on current in other wire.

5. What does the symbol $\mu_0$ represent?

   Permeability of free space. Fundamental constant relating magnetic field to current in vacuum.

6. Calculate the magnetic force on a proton moving perpendicular to a 0.2 T field at $10^7$ m/s.

   $F = 3.2 \times 10^{-13} \, \text{N}$. Using $F = qvB$ with proton charge $1.6 \times 10^{-19}$ C.

7. What is the formula for the magnetic flux through a surface?

   $\Phi_B = \int \mathbf{B} \cdot d\mathbf{A}$. Dot product of magnetic field and area vectors over surface.

8. Calculate the magnetic field due to a long wire carrying 8 A, 0.3 m away.

   $B = 5.33 \times 10^{-6} \, \text{T}$. Using field formula for straight wire at specified distance.

9. Find the magnetic moment of a loop with 5 turns, area $0.01 \, \text{m}^2$, current 2 A.

   $\mu = 0.1 \, \text{A} \cdot \text{m}^2$. Multiple turns multiply the effective current-area product.

10. Calculate the magnetic field inside a solenoid with $n = 1000$ turns/m, $I = 2$ A.

    $B = 2.51 \times 10^{-3} \, \text{T}$. Using $B = \mu_0 n I$ with given turn density and current.

11. Calculate the force on a 2 m wire carrying 3 A in a 0.5 T field at $90^\circ$.

    $F = 3 \, \text{N}$. Using $F = ILB$ since wire is perpendicular to field.

12. What is the relationship between Tesla and Gauss?

    1 T = 10,000 G. Tesla is the larger SI unit; Gauss is the smaller CGS unit.

13. Identify the direction of the force on a positive charge moving in a magnetic field.

    Use right-hand rule: thumb in velocity, fingers in field, palm shows force. Same right-hand rule applies for force direction on positive charges.

14. State Ampère's Law.

    $\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enc}}$. Relates circulation of magnetic field to enclosed current.

15. Identify the direction of the magnetic field around a current-carrying wire.

    Use right-hand rule: thumb in current direction, curl fingers. Fingers curl in direction of field lines around the current.

16. Find the magnetic field strength 0.2 m from a wire carrying 5 A.

    $B = \frac{\mu_0 I}{2\pi r} = 5 \times 10^{-6} \, \text{T}$. Using $B = \frac{\mu_0 I}{2\pi r}$ with given values.

17. Identify the effect of a uniform magnetic field on a stationary charge.

    No force; the charge remains stationary. Magnetic force requires motion; stationary charges experience no magnetic force.

18. What is the cyclotron frequency of a charge $q$ in a magnetic field $B$?

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

19. What happens to the magnetic force if the velocity of a charge is parallel to the field?

    Force is zero. No force when $\sin \theta = 0$ in the force equation.

20. State the Lorentz force law.

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

21. What is the magnetic moment of a loop with area $A$ and current $I$?

    $\mu = I A$. Product of current and enclosed area gives magnetic dipole moment.

22. What is the formula for the force between two parallel current-carrying wires?

    $F = \frac{\mu_0 I_1 I_2 L}{2\pi d}$. Force per unit length between parallel wires separated by distance $d$.

23. State the magnetic field outside a long, straight conductor with current $I$.

    $B = \frac{\mu_0 I}{2\pi r}$. Field decreases inversely with distance from straight current-carrying wire.

24. Find the radius of the circular path of an electron in a 0.1 T field, $v = 10^6$ m/s.

    $r = 5.7 \times 10^{-3} \, \text{m}$. Using $r = \frac{mv}{qB}$ with electron mass and charge values.

25. Calculate the force per unit length between two wires, $I_1 = 5$ A, $I_2 = 10$ A, $d = 0.1$ m.

    $F/L = 1 \times 10^{-4} \, \text{N/m}$. Using force per length formula with given current and separation values.

26. What is the magnetic field of a solenoid with $n$ turns/m and current $I$?

    $B = \mu_0 n I$. Field inside long solenoid is uniform and proportional to turn density.

27. Identify the unit of magnetic moment.

    Ampere-square meters ($\text{A} \cdot \text{m}^2$). SI unit combining current and area for magnetic dipole strength.

28. State the Biot-Savart Law.

    $d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{r}}{r^3}$. Law for calculating magnetic field from any current distribution.

29. What is the formula for the magnetic field at the center of a circular loop?

    $B = \frac{\mu_0 I}{2R}$. Field strength at the center of a current loop with radius $R$.

30. What is the energy density of a magnetic field with strength $B$?

    $u = \frac{B^2}{2\mu_0}$. Energy stored per unit volume in magnetic field.

31. Find the magnetic force on a charge $q = 1.6 \times 10^{-19}$ C, $v = 10^6$ m/s, $B = 0.1$ T.

    $F = 1.6 \times 10^{-14} \, \text{N}$. Using $F = qvB$ for perpendicular motion in magnetic field.

32. What is the torque on a loop with magnetic moment $\mu$ in a field $B$?

    $\tau = \mu B \sin \theta$. Torque depends on magnetic moment, field strength, and orientation angle.

33. What is the force on a charge $q$ moving in a perpendicular magnetic field $B$?

    $F = qvB$. Simplified formula when velocity is perpendicular to magnetic field.

34. Describe the path of a charged particle in a uniform magnetic field.

    Circular or helical, depending on initial velocity. Trajectory depends on initial velocity component parallel to field.

35. State the right-hand rule for the direction of the magnetic force.

    Point thumb in velocity, fingers in magnetic field; palm shows force. Standard method for determining direction of magnetic force on moving charges.

36. Identify the SI unit for magnetic field strength.

    Tesla (T). Named after Nikola Tesla, equals one weber per square meter.

37. State the value of the permeability of free space, $\mu_0$.

    $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$. Exact value defined in SI units for magnetic calculations.

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

    $F = qvB \, \sin \theta$. Force depends on charge, velocity, field strength, and angle between velocity and field.

39. What is the effect of a magnetic field on the speed of a charged particle?

    Speed remains constant; direction changes. Magnetic force is always perpendicular to velocity, doing no work.

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