Magnetic Fields - AP Physics C Electricity and Magnetism

1. What is the formula for the energy density of a magnetic field?

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

2. Identify the effect of a magnetic field on a magnetic dipole.

   A torque aligns the dipole with the field. Magnetic torque tends to align dipole moment with field direction.

3. Calculate torque on a loop with $A = 0.1m^2$, $I = 5A$, in $B = 0.2T$.

   $\tau = 0.1Nm$. Using $\tau = \mu B = IAB$ when field perpendicular to loop.

4. Identify the unit for magnetic flux.

   Weber (Wb). Equivalent to tesla-meter squared ($\text{T}\cdot\text{m}^2$).

5. Find magnetic force on a $5m$ wire with $I = 10A$ in $B = 2T$.

   $F = 100N$. Using $F = ILB$ assuming field perpendicular to wire.

6. Determine the direction of the magnetic field inside a solenoid.

   Along the axis of the solenoid. Current creates uniform field parallel to solenoid axis inside.

7. Determine the direction of force on a positive charge moving in a magnetic field.

   Perpendicular to both velocity and magnetic field. Right-hand rule determines force direction from velocity and field vectors.

8. What is the effect of a magnetic field on a stationary charge?

   No force is exerted on a stationary charge. Magnetic force requires motion; stationary charges experience no magnetic force.

9. What is the Lorentz force on a charged particle?

   $F = q(E + v \times B)$. Total electromagnetic force combines electric and magnetic components.

10. State the formula for magnetic flux through a surface.

    $\Phi_B = \int \vec{B} \cdot d\vec{A}$. Dot product integrates normal component of field over surface area.

11. What is the relationship between $B$ and $E$ in electromagnetic waves?

    $E = cB$. Electric and magnetic fields perpendicular in electromagnetic waves.

12. What is Lenz's Law concerning magnetic fields?

    Induced EMF opposes change in magnetic flux. Consequence of energy conservation in electromagnetic induction.

13. What is 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 and geometry.

14. Identify the direction of magnetic field lines around a bar magnet.

    From north pole to south pole outside the magnet. Field lines form closed loops, never intersect, and show field direction.

15. Determine $B$ inside a solenoid with $n = 1000/m$ and $I = 2A$.

    $B = 0.0025T$. Substituting values into $B = \mu_0 n I$ formula.

16. What is the magnetic field at the center of a current loop?

    $B = \frac{\mu_0 I}{2R}$. Field strength inversely proportional to loop radius at center.

17. What is the role of the magnetic field in a cyclotron?

    Keeps charged particles in circular paths. Magnetic force provides centripetal acceleration for circular particle motion.

18. Identify the force on a charge in a uniform magnetic field.

    Centripetal force causing circular motion. Magnetic force always perpendicular to velocity provides centripetal acceleration.

19. Identify the variable $n$ in the solenoid magnetic field formula.

    Number of turns per unit length. Higher turn density creates stronger magnetic field inside solenoid.

20. Identify the relationship between electric and magnetic forces on a charge.

    Magnetic force is perpendicular to velocity; electric force is not. Key difference: magnetic force always perpendicular to motion.

21. Identify the right-hand rule for a current-carrying wire.

    Thumb: current direction; fingers: magnetic field lines. Force direction given by palm when thumb and fingers align correctly.

22. Find the magnetic field due to a long straight current-carrying wire.

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

23. State the formula for the torque on a magnetic dipole in a field.

    $\tau = \mu \times B$. Cross product gives torque magnitude and direction for dipole alignment.

24. What is 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 angle.

25. Calculate magnetic flux through a $1m^2$ area with $B = 2T$.

    $\Phi_B = 2Wb$. Using $\Phi = BA$ when field is perpendicular to surface.

26. What is the magnetic field strength at the center of a solenoid?

    $B = \mu_0 n I$. Field uniform and strongest along central axis of solenoid.

27. What determines the direction of magnetic force on a moving charge?

    Right-hand rule: velocity and magnetic field directions. Cross product $\vec{v} \times \vec{B}$ determines force direction.

28. State the formula for the magnetic force on a moving charge.

    $F = qvB \, \sin \theta$. Force depends on charge, velocity, field strength, and angle between $\vec{v}$ and $\vec{B}$.

29. Determine the magnetic force on a proton at rest in a magnetic field.

    Zero force as velocity is zero. Magnetic force requires velocity; no motion means no force.

30. What is the Hall effect?

    Voltage generated across a conductor by a magnetic field. Charge separation creates voltage perpendicular to current and field.

31. Calculate the magnetic force on an electron with $v = 2 \times 10^6 m/s$ in $B = 0.3T$.

    $F = 9.6 \times 10^{-14} N$. Using $F = qvB$ with electron charge $e = 1.6 \times 10^{-19}$ C.

32. Calculate the force on a charge $q = 2C$ moving at $v = 3m/s$ in $B = 4T$.

    $F = 24N$. Using $F = qvB$ with $\sin 90° = 1$ for perpendicular motion.

33. What is the magnetic field at the edge of a solenoid?

    Approximately zero outside the solenoid. Field lines concentrated inside solenoid, very weak outside.

34. What is the formula for the magnetic dipole moment of a loop?

    $\mu = IA$. Product of current and enclosed area gives magnetic moment strength.

35. What is the SI unit for magnetic field strength?

    Tesla (T). Named after Nikola Tesla, equals $1 \, \text{Wb/m}^2$.

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