Investigate Current and Magnetic Fields - Physics

1. Find the force on a $0.50\ \text{m}$ wire carrying $I=4.0\ \text{A}$ in $B=0.30\ \text{T}$ at $90^\circ$.

   $F=0.60\ \text{N}$. Using $F=BIL\sin 90°=0.30×4.0×0.50×1$.

2. What happens to the magnetic field around a wire if the current doubles?

   The field magnitude doubles. Field is directly proportional to current: $B \propto I$.

3. What is the direction of the force between two parallel wires carrying currents in the same direction?

   They attract each other. Same-direction currents create attractive magnetic forces.

4. What is the direction of the magnetic field inside a current-carrying solenoid?

   Nearly uniform, along the solenoid axis. Field lines are parallel inside, negligible outside ideal solenoid.

5. Identify the direction of $\vec{B}$ at a point above a wire with current into the page.

   $\vec{B}$ points right (clockwise around the wire). Right-hand rule: thumb in, fingers curl clockwise.

6. What is the direction rule for the force on a current in a magnetic field (motor effect)?

   Fleming's left-hand rule. First finger: field, second: current, thumb: force direction.

7. What is the SI unit of magnetic field strength $B$?

   tesla (T). Named after Nikola Tesla; 1 T = 1 N/(A·m).

8. What is the definition of a magnetic field line direction at a point?

   Direction of the force on a north pole (or compass north end) at that point. Field lines show path a free north pole would follow.

9. What is the SI unit of magnetic flux density $B$?

   tesla (T). Named after Nikola Tesla; 1 T = 1 Wb/m² = 1 N/(A·m).

10. What rule gives the magnetic field direction around a straight wire from the current direction?

    Right-hand grip rule. Thumb along current, fingers curl around wire showing field lines.

11. What is the magnetic field direction at the center of a circular current loop?

    Along the loop axis, given by the right-hand rule. Fingers follow current, thumb points through loop center.

12. Find the force on a charge $q=2.0\times10^{-6}\ \text{C}$ moving at $v=3.0\times10^{5}\ \text{m/s}$ in $B=0.20\ \text{T}$ at $90^\circ$.

    $F=0.12\ \text{N}$. Using $F=qvB\sin 90°=2.0×10^{-6}×3.0×10^5×0.20×1$.

13. State the formula for the magnetic field inside a long solenoid with $n$ turns per meter.

    $B=\mu_0 n I$. Uniform field inside; $n$ is turns per unit length.

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

    Perpendicular to both $\vec{v}$ and $\vec{B}$. Use right-hand rule: fingers $\vec{v}$ to $\vec{B}$, thumb shows force.

15. What is the formula for $B$ at the center of a single circular loop of radius $R$?

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

16. State the formula for the magnetic field at the center of a circular loop of radius $R$.

    $B=\frac{\mu_0 I}{2R}$. Field at loop center is half that of straight wire at same distance.

17. What is the formula for the force on a straight wire of length $L$ in a uniform field $B$?

    $F=BIL\sin\theta$. $\theta$ is angle between current and field directions.

18. What is the formula for the force on a moving charge $q$ with speed $v$ in a magnetic field $B$?

    $F=qvB\sin\theta$. Lorentz force law; $\theta$ is angle between velocity and field.

19. Find the magnetic field at $r=0.20\ \text{m}$ from a long wire carrying $I=10\ \text{A}$.

    $B=1.0\times10^{-5}\ \text{T}$. Using $B=\frac{\mu_0 I}{2\pi r}=\frac{4\pi×10^{-7}×10}{2\pi×0.20}$.

20. State the formula for magnetic field magnitude at distance $r$ from a long straight wire.

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

21. What is the direction of the magnetic field inside a solenoid relative to its coils?

    Along the solenoid axis, from its south end to its north end inside. Field lines run straight through the solenoid's interior.

22. Identify the condition for maximum force on a current-carrying wire in a magnetic field.

    When $\theta=90^\circ$ (wire perpendicular to $B$). $\sin 90° = 1$ gives maximum force magnitude.

23. Find $F$ when $B=0.50\ \text{T}$, $I=2.0\ \text{A}$, $L=0.30\ \text{m}$, $\theta=90^\circ$.

    $F=0.30\ \text{N}$. $F = 0.50 \times 2.0 \times 0.30 \times \sin(90°) = 0.30$ N.

24. What is the direction of the force between two parallel wires carrying currents in opposite directions?

    They repel each other. Opposite currents create repulsive magnetic forces.

25. Identify how $B$ inside a long solenoid changes if the turn density $n$ doubles (same $I$).

    $B$ doubles. $B$ is directly proportional to turn density $n$.

26. Identify the force on a wire if it is parallel to $\vec{B}$ (so $\theta=0^\circ$).

    $F=0\ \text{N}$. $\sin(0°) = 0$, so no force when wire parallel to field.

27. What happens to $B$ around a long straight wire if the distance $r$ from the wire doubles?

    It halves, since $B\propto\frac{1}{r}$. Field follows inverse relationship with radial distance.

28. What is the direction of the magnetic field around a straight current-carrying wire?

    Concentric circles around the wire. Thumb points along current, fingers curl in field direction.

29. Identify how $B$ changes if the distance from a long straight wire doubles (same $I$).

    $B$ halves. $B$ is inversely proportional to distance $r$.

30. Identify the direction of $\vec{B}$ at a point to the right of a wire with current out of the page.

    $\vec{B}$ points upward (counterclockwise around the wire). Right-hand rule: thumb out, fingers curl counterclockwise.

31. What is the formula for magnetic field magnitude at distance $r$ from a long straight wire?

    $B=\frac{\mu_0 I}{2\pi r}$. Field decreases with distance from wire, proportional to current.

32. What is the relationship between field-line spacing and magnetic field strength?

    Closer field lines indicate a stronger $B$. Field line density represents field magnitude visually.

33. Identify how $B$ changes if the current in a long straight wire doubles (same $r$).

    $B$ doubles. $B$ is directly proportional to current $I$.

34. What is the direction of the force on a current in a magnetic field (motor effect rule)?

    Fleming left-hand rule: index $\vec{B}$, middle $I$, thumb $\vec{F}$. Three fingers perpendicular: force, field, and current directions.

35. What is the value of the permeability of free space $\mu_0$?

    $\mu_0=4\pi\times10^{-7}\ \text{T·m/A}$. Fundamental constant relating magnetic field to current in vacuum.

36. What is the direction rule for the magnetic field around a straight current-carrying wire?

    Right-hand grip rule: thumb $I$, curled fingers give $\vec{B}$ direction. Fingers curl in the direction of circular field lines around wire.

37. State the formula for the magnetic force on a straight wire of length $L$ in field $B$.

    $F=BIL\sin\theta$. $\theta$ is angle between wire and field; max force at $90°$.

38. What is the value of the permeability of free space $\mu_0$ (in SI units)?

    $\mu_0=4\pi\times10^{-7}\ \text{T·m/A}$. Fundamental constant relating magnetic fields to currents.

39. What is the formula for the field inside a long solenoid with $n$ turns per meter?

    $B=\mu_0 n I$. Field strength depends on turn density and current, not length.

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