3a) Explain the motion of (a) a static electron, and (b) an electron in motion, under the influence of an applied magnetic field.
3a) Explain the motion of (a) a static electron, and (b) an electron in motion, under the influence of an applied magnetic field.
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![**Physics Problem**
**Question 3a**
Explain the motion of (a) a static electron, and (b) an electron in motion, under the influence of an applied magnetic field.
**Question 3b**
Given the electric field:
\[ E = \frac{1}{\pi \epsilon_0 r^7} (a_r \cos \theta \cos \phi + a_{\theta} \sin \theta \cos \phi) \]
Find:
(a) The volume charge density.
(b) The total charge in the region shown using both sides of Gauss's law.
**Diagram Explanation:**
The diagram depicts a spherical coordinate system with the coordinates \(x, y,\) and \(z\) labeled. The sphere has a radius of 2 units.
- The \(x\)-axis extends horizontally to the right.
- The \(y\)-axis extends horizontally to the left.
- The \(z\)-axis extends vertically.
The drawing includes:
1. A quarter-sphere with a radius of 2 units.
2. Dashed lines representing the coordinate axes' intersections with the sphere's surface.
This setup is used to determine the total charge within the given volume using Gauss's law.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc31f934b-62b7-425c-8b5d-bfb0b333f649%2F335ad30c-3daf-4a5c-93fd-212adc937376%2Fk8y6cp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Problem**
**Question 3a**
Explain the motion of (a) a static electron, and (b) an electron in motion, under the influence of an applied magnetic field.
**Question 3b**
Given the electric field:
\[ E = \frac{1}{\pi \epsilon_0 r^7} (a_r \cos \theta \cos \phi + a_{\theta} \sin \theta \cos \phi) \]
Find:
(a) The volume charge density.
(b) The total charge in the region shown using both sides of Gauss's law.
**Diagram Explanation:**
The diagram depicts a spherical coordinate system with the coordinates \(x, y,\) and \(z\) labeled. The sphere has a radius of 2 units.
- The \(x\)-axis extends horizontally to the right.
- The \(y\)-axis extends horizontally to the left.
- The \(z\)-axis extends vertically.
The drawing includes:
1. A quarter-sphere with a radius of 2 units.
2. Dashed lines representing the coordinate axes' intersections with the sphere's surface.
This setup is used to determine the total charge within the given volume using Gauss's law.
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