Magnetism and Current-Carrying Wires - AP Physics 2

1. Calculate the force between two parallel wires $2 \text{ m}$ apart carrying $4 \text{ A}$ each.

   $1.6 \times 10^{-6}$ N. Use force formula with $d=2m$ and $I_1=I_2=4A$.

2. What is the magnetic force direction on a wire with current in a magnetic field?

   Perpendicular to both current and field. Force follows right-hand rule for current and field vectors.

3. State the formula for the magnetic field due to a moving point charge.

   $B = \frac{\mu_0 q v \times \hat{r}}{4 \pi r^2}$. Moving charge creates magnetic field like current element.

4. What is the magnetic force on a charged particle moving parallel to a magnetic field?

   Zero. No perpendicular component means no magnetic force.

5. Identify the unit for electric current.

   Ampere (A). Ampere measures electric current flow rate.

6. What is the magnetic field direction around a long straight current-carrying wire?

   Circular around the wire. Current creates concentric circular field lines around the wire.

7. Calculate the magnetic force on a $2 \text{ C}$ charge moving at $3 \text{ m/s}$ perpendicular to a $4 \text{ T}$ field.

   $24$ N. Use $F = qvB$ with perpendicular motion and field.

8. Find the magnetic field at the center of a loop with $5 \text{ A}$ and radius $0.1 \text{ m}$.

   $10^{-5}$ T. Use $B = \frac{\mu_0 I}{2R}$ with given values.

9. What is the permeability of free space $\mu_0$ in Tm/A?

   $4\pi \times 10^{-7}$ Tm/A. Fundamental constant relating magnetic field to current.

10. What fundamental quantity creates a magnetic field in a wire?

    Electric current. Moving charges (current) generate magnetic fields.

11. Find the magnetic dipole moment of a $10$-turn coil with $2 \text{ A}$ current and $0.5 \text{ m}^2$ area.

    $10 \text{ A m}^2$. Use $\mu = NIA$ with $N=10$, $I=2 \text{A}$, $A=0.5 \text{m}^2$.

12. What is the torque on a current loop in a uniform magnetic field?

    $\tau = \mu B \sin(\theta)$. Torque depends on magnetic moment and field angle.

13. State the Biot-Savart Law for a small segment of current-carrying wire.

    $dB = \frac{\mu_0}{4\pi} \frac{I \, d\ell \times \hat{r}}{r^2}$. Fundamental law for calculating magnetic fields from current elements.

14. Determine the magnetic force on a $0.5 \text{ C}$ charge moving at $4 \text{ m/s}$ in a $1 \text{ T}$ field.

    $2$ N. Use $F = qvB$ with $q=0.5C$, $v=4m/s$, $B=1T$.

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

    $B = \frac{\mu_0 I}{2R}$. Field at center depends on current and radius.

16. State 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 carrying current.

17. Identify the relationship between current direction and magnetic field in a wire.

    Right-hand grip rule. Curl fingers in current direction, thumb points along magnetic field.

18. State the unit of magnetic field strength.

    Tesla (T). Tesla is the SI unit for magnetic field strength.

19. What is the relationship between magnetic field strength and distance from a wire?

    Inversely proportional. Field strength decreases as $\frac{1}{r}$ from the wire.

20. Calculate the magnetic force on a wire with $3 \text{ A}$ current and $1 \text{ m}$ length in a $2 \text{ T}$ field.

    $6$ N. Use $F = ILB$ with perpendicular orientation.

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

    $F = I L B \, \sin(\theta)$. Force equals current times length times magnetic field times sine of angle.

22. What is the direction of the magnetic field inside a solenoid?

    Parallel to the axis. Solenoid creates uniform field along its central axis.

23. What is the effect of doubling the velocity of a charged particle on the magnetic force it experiences?

    Doubles the force. Force is directly proportional to particle velocity.

24. What is the direction of the force on a negative charge in a magnetic field?

    Opposite to right-hand rule. Negative charge reverses the force direction from right-hand rule.

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

    Right-hand rule. Point fingers in velocity direction, curl toward field, thumb shows force.

26. What is the effect on the magnetic field if the number of turns in a solenoid is doubled?

    Doubles. Field strength is directly proportional to number of turns.

27. What happens to the magnetic field strength if the current in a wire doubles?

    Doubles. Magnetic field is directly proportional to current.

28. Determine the force on a $1.5 \text{ m}$ wire with $4 \text{ A}$ current parallel to a $0.2 \text{ T}$ field.

    $0$ N. Parallel orientation gives $\sin(0°) = 0$, so no force.

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

    $B = \mu_0 n I$. Field depends on turns per length and current.

30. Find the magnetic force on a $2 \text{ m}$ wire with $3 \text{ A}$ current in $0.5 \text{ T}$ field.

    $3$ N. Use $F = ILB$ with $I=3A$, $L=2m$, $B=0.5T$.

31. State the formula for the magnetic dipole moment of a coil.

    $\mu = NIA$. Product of turns, current, and loop area.

32. What is the effect of temperature on the magnetization of ferromagnetic materials?

    Decreases with increasing temperature. Higher temperature reduces magnetic alignment in ferromagnets.

33. Determine the magnetic force on a $1 \text{ C}$ charge moving at $2 \text{ m/s}$ in a $3 \text{ T}$ field.

    $6$ N. Use $F = qvB$ with $q=1C$, $v=2m/s$, $B=3T$.

34. What is the effect of a magnetic field on an electron at rest?

    No effect. Magnetic force requires motion of charged particle.

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