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0. Math Review31m
- Math Review
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1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
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14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
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18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

29. Sources of Magnetic Field

Magnetic Field Produced by Moving Charges

Physics

29. Sources of Magnetic Field

Magnetic Field Produced by Moving Charges

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Multiple Choice

As a proton passes the origin, its velocity is $3.0 \times 10^{5} m / s$ in the positive x direction. What is the magnitude of the magnetic field at the point ( $12.0 cm$ , $5.0 cm$ , $0.0 cm$ )?

1.2 \times 10^{- 20} T

5.2 \times 10^{- 20} T

9.2 \times 10^{- 20} T

1.8 \times 10^{- 19} T

2.4 \times 10^{- 19} T

1.1 x 10^-19T

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Verified step by step guidance

Identify the relevant formula for the magnetic field due to a moving charge, which is given by the Biot-Savart Law: $ \mathbf{B} = \frac{\mu_0}{4\pi} \frac{q \mathbf{v} \times \mathbf{r}}{r^3} $, where $ \mathbf{B} $ is the magnetic field, $ \mu_0 $ is the permeability of free space, $ q $ is the charge, $ \mathbf{v} $ is the velocity, and $ \mathbf{r} $ is the position vector from the charge to the point of interest.

Convert the position coordinates from centimeters to meters for consistency in SI units: $ (12.0\, \text{cm}, 5.0\, \text{cm}, 0.0\, \text{cm}) $ becomes $ (0.12\, \text{m}, 0.05\, \text{m}, 0.0\, \text{m}) $.

Calculate the position vector $ \mathbf{r} $ from the origin to the point of interest: $ \mathbf{r} = (0.12\, \text{m}, 0.05\, \text{m}, 0.0\, \text{m}) $. The magnitude $ r $ is given by $ r = \sqrt{(0.12)^2 + (0.05)^2 + (0.0)^2} $.

Determine the cross product $ \mathbf{v} \times \mathbf{r} $. Since $ \mathbf{v} = (3.0 \times 10^5\, \text{m/s}, 0, 0) $ and $ \mathbf{r} = (0.12, 0.05, 0) $, the cross product is calculated using the determinant: $ \mathbf{v} \times \mathbf{r} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 3.0 \times 10^5 & 0 & 0 \\ 0.12 & 0.05 & 0 \end{vmatrix} $.

Substitute the values into the Biot-Savart Law to find the magnitude of the magnetic field $ B $: $ B = \frac{\mu_0}{4\pi} \frac{q \| \mathbf{v} \times \mathbf{r} \|}{r^3} $. Use the known values for $ \mu_0 $, the charge of a proton $ q = 1.6 \times 10^{-19}\, \text{C} $, and the calculated $ \| \mathbf{v} \times \mathbf{r} \| $ and $ r $.