A +5.0@mC charge experiences a 0.64-N force in the positive y direction. If this charge is replaced with a -2.7@mC charge, what force will it experience?

The force experienced by a charge in an electric field \( \mathbf{E} \) is given by:

\[
\mathbf{F} = q \mathbf{E}
\]

Where:
- \( \mathbf{F} \) is the force on the charge,
- \( q \) is the charge, and
- \( \mathbf{E} \) is the electric field.

First, we calculate the electric field using the given force and charge of \( +5.0 \, \text{mC} \):

\[
\mathbf{E} = \frac{\mathbf{F}}{q}
\]

Given:
- \( \mathbf{F} = 0.64 \, \text{N} \) (in the positive y direction),
- \( q = 5.0 \, \text{mC} = 5.0 \times 10^{-3} \, \text{C} \).

Thus:

\[
\mathbf{E} = \frac{0.64 \, \text{N}}{5.0 \times 10^{-3} \, \text{C}} = 128 \, \text{N/C}
\]

Now, when the charge is replaced with a \( -2.7 \, \text{mC} \) charge, the force will be:

\[
\mathbf{F} = q \mathbf{E}
\]

Where:
- \( q = -2.7 \, \text{mC} = -2.7 \times 10^{-3} \, \text{C} \),
- \( \mathbf{E} = 128 \, \text{N/C} \).

Thus:

\[
\mathbf{F} = (-2.7 \times 10^{-3} \, \text{C}) \times 128 \, \text{N/C} = -0.3456 \, \text{N}
\]

The negative sign indicates the force is in the opposite direction of the electric field. Since the electric field was in the positive y direction, the force on the \( -2.7 \, \text{mC} \) charge will be:

\[
\mathbf{F} = 0.3456 \, \text{N} \, \text{in the negative y direction}.
\]

### Summary:
If the charge is replaced with a \( -2.7 \, \text{mC} \) charge, it will experience a force of \( 0.3456 \, \text{N} \) in the negative y direction.

Do you need more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How is the direction of force determined in an electric field?
2. What is the relationship between electric field strength and the force on a charge?
3. How would the force change if the charge were doubled?
4. What happens to the force if the charge is positioned in a uniform vs. non-uniform electric field?
5. How does the electric field between two point charges behave?

**Tip:** The sign of a charge affects the direction of the force but not its magnitude if the electric field is constant.

A +5.0 mC charge experiences a 0.64-N force in the positive y direction. If this charge is replaced with a -2.7 mC charge, what force will it experience?

Understand how to calculate the force on a charge when placed in an electric field. This example calculates the electric field based on a 5.0 mC charge and a 0.64-N force and then finds the force on a -2.7 mC charge in the same field. Suitable for high school physics students.

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