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Suppose I have a uniformly charged spherical shell with charge density [tex]\(\sigma\)[/tex]. I place a point charge inside the shell, slightly off center. Which of the following statements is true?

1. The particle will feel a non-zero net force away from the center point.
2. The particle will feel zero net force.
3. The particle will feel a non-zero net force towards the center point.

Sagot :

Certainly! Let's analyze the problem step by step.

### Step 1: Understanding the setup
- We have a uniformly charged spherical shell with a surface charge density denoted by [tex]\(\sigma\)[/tex].
- A point charge is placed inside this spherical shell but not at the center; instead, it is slightly off-center.

### Step 2: Application of Gauss's Law
- Gauss's law for electricity states that the electric flux through a closed surface is proportional to the charge enclosed by the surface.
- For a point charge inside a spherical shell (given uniform charge distribution), we need to consider the electric field due to the shell's charges.

### Step 3: Analyzing the Electric Field Inside the Shell
- A key result from electrostatics is that a uniformly charged spherical shell produces no net electric field at any point inside the shell. This is because the contributions to the electric field from different parts of the charged shell cancel out.

### Step 4: Net Force on the Point Charge
- Since the electric field inside the uniformly charged spherical shell is zero, any charge placed inside will experience no net electrostatic force. This result holds irrespective of the position of the point charge inside the shell.

### Conclusion
- Given all points above, the point charge inside the uniformly charged spherical shell will feel zero net force.

Thus, the correct statement is:
2. The particle will feel zero net force.