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particle with positive charge qqq is moving with speed v along the z axis toward positive z. At the time of this problem it is located at the origin, x=y=z=0. Your task is to find the magnetic field at various locations in the three-dimensional space around the moving charge. (a) Which of the following expressions gives the magnetic field at the point r→ due to the moving charge? (b) Find the magnetic field at the point r1 = x1i. (c) Find the magnetic field at the point r2 = y1j. (d) Find the magnetic field at the point r3 = x1i + z1k.

particle with positive charge qqq is moving with speed v along the z axis toward positive z. At the time of this problem it is located at the origin, x=y=z=0. Your task is to find the magnetic field at various locations in the three-dimensional space around the moving charge. (a) Which of the following expressions gives the magnetic field at the point r→ due to the moving charge? (b) Find the magnetic field at the point r1 = x1i. (c) Find the magnetic field at the point r2 = y1j. (d) Find the magnetic field at the point r3 = x1i + z1k.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A particle with positive charge qqq is moving with speed v along the z axis toward positive z. At the time of this problem it is located at the origin, x=y=z=0. Your task is to find the magnetic field at various locations in the three-dimensional space around the moving charge.

(a) Which of the following expressions gives the magnetic field at the point r→ due to the moving charge?

(b) Find the magnetic field at the point r1 = x1i.

(c) Find the magnetic field at the point r2 = y1j.

(d) Find the magnetic field at the point r3 = x1i + z1k.

(e) The field found in this problem for a moving charge is the same as the field from a current element of length dldldl carrying current i provided that the quantity qv is replaced by which quantity?

 

The image illustrates a 3-dimensional coordinate system with axes labeled \(x\), \(y\), and \(z\). At the origin, there is a point labeled \(q\) with a positive charge, represented by a red circle containing a plus sign. There is a vector \(\vec{v}\) shown as a green arrow pointing upwards along the \(z\)-axis, indicating the direction of velocity or another vectorial quantity. Three points are indicated in the diagram: - A point along the \(z\)-axis at a distance \(z_1\) from the origin. - A point along the \(x\)-axis at a distance \(x_1\). - A point along the \(y\)-axis at a distance \(y_1\). Additionally, there is a highlighted point in space, represented by the coordinates \((x_1, 0, z_1)\). This point is connected to the respective axes by dashed lines, illustrating its position relative to the \(x\)- and \(z\)-axes. The horizontal and vertical distances from this point to the \(x\)- and \(z\)-axes are shown as \(x_1\) and \(z_1\). This diagram can be used to explore concepts related to electromagnetism, vector fields, or coordinate geometry.
Transcribed Image Text:The image illustrates a 3-dimensional coordinate system with axes labeled \(x\), \(y\), and \(z\). At the origin, there is a point labeled \(q\) with a positive charge, represented by a red circle containing a plus sign. There is a vector \(\vec{v}\) shown as a green arrow pointing upwards along the \(z\)-axis, indicating the direction of velocity or another vectorial quantity. Three points are indicated in the diagram: - A point along the \(z\)-axis at a distance \(z_1\) from the origin. - A point along the \(x\)-axis at a distance \(x_1\). - A point along the \(y\)-axis at a distance \(y_1\). Additionally, there is a highlighted point in space, represented by the coordinates \((x_1, 0, z_1)\). This point is connected to the respective axes by dashed lines, illustrating its position relative to the \(x\)- and \(z\)-axes. The horizontal and vertical distances from this point to the \(x\)- and \(z\)-axes are shown as \(x_1\) and \(z_1\). This diagram can be used to explore concepts related to electromagnetism, vector fields, or coordinate geometry.
### Physics Problem: Vector Calculations Consider the following expressions, where each option represents an equation involving vectors, constants, and cross products. **Expressions:** A. \(\frac{\mu_0}{4\pi} \frac{\vec{qv} \times \hat{r}}{r^2}\) B. \(\frac{\mu_0}{4\pi} \frac{q\vec{v} \times \vec{r}}{r^3}\) C. \(\frac{\mu_0}{4\pi} \frac{q\hat{r} \times \vec{v}}{r^2}\) D. \(\frac{\mu_0}{4\pi} \frac{\vec{qr} \times \vec{v}}{r^3}\) **Multiple Choice Options:** - A only - B only - C only - D only - both A and B - both C and D - both A and C - both B and D **Selected Answer:** - A only This multiple choice question requires analyzing each mathematical expression, especially focusing on the vector cross-products and the powers of \(r\) in the denominators, to determine which one(s) satisfy a given condition. The selected answer is "A only."
Transcribed Image Text:### Physics Problem: Vector Calculations Consider the following expressions, where each option represents an equation involving vectors, constants, and cross products. **Expressions:** A. \(\frac{\mu_0}{4\pi} \frac{\vec{qv} \times \hat{r}}{r^2}\) B. \(\frac{\mu_0}{4\pi} \frac{q\vec{v} \times \vec{r}}{r^3}\) C. \(\frac{\mu_0}{4\pi} \frac{q\hat{r} \times \vec{v}}{r^2}\) D. \(\frac{\mu_0}{4\pi} \frac{\vec{qr} \times \vec{v}}{r^3}\) **Multiple Choice Options:** - A only - B only - C only - D only - both A and B - both C and D - both A and C - both B and D **Selected Answer:** - A only This multiple choice question requires analyzing each mathematical expression, especially focusing on the vector cross-products and the powers of \(r\) in the denominators, to determine which one(s) satisfy a given condition. The selected answer is "A only."
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