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To solve for the angle \(\theta\), we need to analyze the forces acting on the charge in equilibrium.

### Given Data:
- Electric field, \( \vec{E} = 200,000 \, \text{N/C} \)
- Charge, \( q = 25 \, \text{nC} = 25 \times 10^{-9} \, \text{C} \)
- Mass of the charge, \( m = 2.0 \, \text{g} = 0.002 \, \text{kg} \)

### Analysis:
1. **Electric Force**: The electric field exerts a force \( \vec{F}_e \) on the charge, given by:
   \[
   F_e = qE
   \]
   Plugging in the values:
   \[
   F_e = (25 \times 10^{-9} \, \text{C})(200,000 \, \text{N/C}) = 0.005 \, \text{N}
   \]

2. **Gravitational Force**: The weight of the mass is:
   \[
   F_g = mg
   \]
   where \( g = 9.8 \, \text{m/s}^2 \).
   \[
   F_g = (0.002 \, \text{kg})(9.8 \, \text{m/s}^2) = 0.0196 \, \text{N}
   \]

3. **Equilibrium Condition**: In equilibrium, the tension in the string will have components balancing the gravitational force vertically and the electric force horizontally.

   For the horizontal and vertical components of the tension \( T \), we have:
   \[
   T \sin \theta = F_e
   \]
   \[
   T \cos \theta = F_g
   \]

   Dividing these equations to eliminate \( T \):
   \[
   \tan \theta = \frac{F_e}{F_g}
   \]

4. **Calculate \(\theta\)**:
   \[
   \theta = \arctan \left( \frac{F_e}{F_g} \right)
   \]
   Substituting \( F_e = 0.005 \, \text{N} \) and \( F_g = 0.0196 \, \text{N} \):
   \[
   \theta = \arctan \left( \frac{0.005}{0.0196} \right)
   \]

   Calculating this:
   \[
   \theta \approx 14.36^\circ
   \]

### Answer:
The angle \(\theta\) is approximately \(14.36^\circ\).

Would you like further details or have any questions?

### Related Questions:
1. How does changing the electric field affect the angle \(\theta\)?
2. What would happen to \(\theta\) if the mass of the charge were doubled?
3. How is the direction of the electric field related to the angle of suspension?
4. If the charge were negative, how would the angle \(\theta\) change?
5. What would be the angle if the electric field strength were decreased to \(100,000 \, \text{N/C}\)?

### Tip:
For equilibrium problems with forces at an angle, breaking down forces into components along orthogonal axes simplifies the solution.

An electric field \( \vec{E} = 200,000 \, \text{N/C} \) causes the point charge in the following figure to hang at an angle. What is \( \theta \)?

Calculate the angle \( \theta \) at which a 25 nC charge, with a mass of 2.0 g, hangs in a 200,000 N/C electric field. This solution covers electrostatic force, gravitational force, and equilibrium analysis.

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