Magnetostatics in Free space

Overview - Lesson 1

Introduction - Lesson 2

Magnetic Flux Density - Lesson 3

No Magnetic Monopoles - Lesson 4

The Solenoidal Law - Lesson 5

Ampere's Law - Lesson 6

Magnetic Vector Potential - Lesson 7

Magnetic Force on Moving Charge - Lesson 8

The Biot Savart Law - Lesson 9

Magnetic Scalar Potential - Lesson 10

Summary - Lesson 11

Practice Problems, Homeworks, and Quiz

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Quiz - Magnetostatics in Free Space

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Quiz - Magnetostatics in Free Space

Magnetostatics in Free space Practice Problems, Homeworks, and Quiz Quiz - Magnetostatics in Free Space

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Question 1 of 10

1. Question
True or False: Magnetic Flux density, $\overline{B}$, is a vector field which imbues the space it occupies with the ability to apply force to any charge
- True
- False
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Question 2 of 10

2. Question
True or False: Magnetic fields can be caused by an electric current
- True
- False
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Question 3 of 10

3. Question
True or False: Magnetic monopoles are the most basic type of magnetic field sources
- True
- False
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Question 4 of 10

4. Question
True or False: The magnetic vector potential, $\overline{A}$, is defined as $\overline{B}=\nabla\times\overline{A}$
- True
- False
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Question 5 of 10

5. Question
True or False: $\overline{H}$ and $\overline{B}$ are both representations of the magnetic field.
- True
- False
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Question 6 of 10

6. Question
True or False: The Lorentz Force Law describes only the force of magnetic fields on a charged particle
- True
- False
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Question 7 of 10

7. Question
Find the magnetic flux density at the center of a circular current loop with radius r, positioned in the x-y plane and symmetric about the z-axis, as shown below.
- $\overline{B}=\frac{\mu_\circ I^2}{2r}\hat{a}_z$
- $\overline{B}=\frac{\mu_\circ I}{4\pi r^2}\hat{a}_z$
- $\overline{B}=\frac{\mu_\circ I}{2r}\hat{a}_z$
- $\overline{B}=\frac{\mu_\circ I}{4\pi r^2}\hat{a}_y$
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Question 8 of 10

8. Question
If an electric charge with charge $Q=1$ travels at velocity $\overline{U} = 1\hat{a}_x + 3\hat{a}_y+2\hat{a}_z$ in a region with electric field $\overline{E} =\frac{4}{3}x^2\hat{a}_x + 2xz\hat{a}_y+y^2\hat{a}_z $, and magnetic flux density $\overline{B}=x^2\hat{a}_x+y^2\hat{a}_y+z^2\hat{a}_z$, what is the force experienced by the charge?
- $\overline{F}=(x+y+3z)\hat{a}_x+\left(7x^2-2z^2+2xyz\right)\hat{a}_y+\left(2y^2z+5x^2y\right)\hat{a}_z$
- $\overline{F}=\left(\frac{4}{3}x^2-2y^2+3z^2\right)\hat{a}_x+\left(2x^2-z^2+2xz\right)\hat{a}_y+\left(2y^2-3x^2\right)\hat{a}_z$
- $\overline{F}=\left(x^2-3y^3+3z\right)\hat{a}_x+\left(x+z^2-5y\right)\hat{a}_y+\left(10xy\right)\hat{a}_z$
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Question 9 of 10

9. Question
Given a current $\overline{J}=J_\circ\frac{1}{zy}\hat{a}_x$ traveling along an infinitely thin wire along the x-axis in free space, find the differential vector potential at a the location given by $a=x\hat{a}_x+y\hat{a}_y+z\hat{a}_z$.
- $\overline{dA}=\frac{\mu_\circ J_\circ yz}{2\sqrt{(x-x^\prime)^2+y^{2}+z^{2}}}\hat{a}_x$
- $\overline{dA}=\frac{\mu_\circ J_\circ dx^\prime}{4\pi zy\sqrt{(x-x^\prime)^2+y^{2}+z^{2}}}\hat{a}_x$
- $\overline{dA}=\frac{2\pi}{\mu_\circ J_\circ \sqrt{x^{\prime 2}+y^{\prime 2}+z^{\prime 2}}}\hat{a}_x$
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Question 10 of 10

10. Question
Given a sheet of current with current density $\overline{J} = b\hat{a}_x$, extending infinitely in both x and y and located at z=0, find the magnetic field in the region above the sheet.
- $\overline{H}=-\frac{b}{2}\hat{a}_y$
- $\overline{H}=\frac{b^2}{4}\hat{a}_y$
- $\overline{H}=\frac{b+1}{2\pi}\hat{a}_y$
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