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The problem provided asks for the magnitude of a charged particle's charge, given that it produces an electric field of 2.0 N/C at a distance of 50 cm from the particle.

The electric field \(E\) due to a point charge is given by Coulomb's law:

\[
E = \frac{k \cdot |q|}{r^2}
\]

where:
- \(E = 2.0 \, \text{N/C}\) (the electric field),
- \(k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2\) (Coulomb's constant),
- \(r = 50 \, \text{cm} = 0.50 \, \text{m}\) (the distance from the particle),
- \(|q|\) is the magnitude of the charge, which we need to find.

Now, we can rearrange the formula to solve for \(|q|\):

\[
|q| = \frac{E \cdot r^2}{k}
\]

Let me calculate the value of \(|q|\).The magnitude of the particle's charge is approximately \( 5.56 \times 10^{-11} \, \text{C} \).

Would you like further details or have any questions about this? Here are some follow-up questions:

1. How does the distance affect the electric field produced by a charge?
2. What is the relationship between electric field strength and charge magnitude?
3. How would the electric field change if the charge was doubled?
4. What units are used for measuring charge and electric field?
5. How does Coulomb's constant relate to electric force calculations?

**Tip:** When solving problems involving Coulomb's law, remember that the electric field decreases with the square of the distance from the charge.

A charged particle produces an electric field with a magnitude of 2.0 N/C at a point that is 50 cm away from the particle. What is the magnitude of the particle's charge?

Learn how to calculate the magnitude of a charged particle's charge given that it produces an electric field of 2.0 N/C at a distance of 50 cm. This problem involves using Coulomb's law and is suitable for students in Grades 11-12.

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