https://file.aiquickdraw.com/mathbot/file/17274488116489kzu10v6.pdf

Проанализируй файл и реши номер 3 и 14. пиши подробно с полным объяснением 

### Problem 3: Electric Field Due to Protons in a Plutonium-239 Nucleus

#### Given:
- Number of protons \( N = 94 \)
- Charge of a single proton \( e = 1.60 \times 10^{-19} \, C \)
- Radius of the nucleus \( R = 6.64 \, \text{fm} = 6.64 \times 10^{-15} \, \text{m} \)

The problem asks for the magnitude and direction of the electric field at the surface of the nucleus. We assume the charge is uniformly distributed.

#### Step 1: Total Charge in the Nucleus
The total charge \( Q \) of the nucleus is given by:
\[
Q = N \times e = 94 \times (1.60 \times 10^{-19}) = 1.504 \times 10^{-17} \, C
\]

#### Step 2: Electric Field at the Surface of a Uniformly Charged Sphere
For a uniformly charged sphere, the electric field at a distance \( r \) from the center (outside the sphere, where \( r = R \)) behaves as though all the charge were concentrated at the center. Thus, the electric field at the surface is:
\[
E = \frac{1}{4\pi \epsilon_0} \frac{Q}{R^2}
\]
Where:
- \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2 \)
- \( Q = 1.504 \times 10^{-17} \, \text{C}

Проанализируй файл и реши номер 3 и 14. пиши подробно с полным объяснением

Detailed solutions to Problem 3 and Problem 14, involving the electric field produced by protons in a plutonium-239 nucleus and the net electric field between two charged particles fixed to an x-axis. Concepts include Coulomb’s law and the superposition principle, suitable for undergraduate physics students.

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