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.
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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