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25. A 10.0-g piece of Styrofoam carries a net charge of AMT -0.700 µC and is suspended in equilibrium above the center of a large, horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge ner unit area on the plastic sheet?

25. A 10.0-g piece of Styrofoam carries a net charge of AMT -0.700 µC and is suspended in equilibrium above the center of a large, horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge ner unit area on the plastic sheet?

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**Problem 25:** A 10.0-g piece of Styrofoam carries a net charge of -0.700 μC and is suspended in equilibrium above the center of a large, horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet? --- **Explanation:** In this scenario, a piece of Styrofoam with a given net charge is suspended above a plastic sheet due to electrostatic forces. The equilibrium condition implies that the electrostatic force exerted by the charged sheet on the Styrofoam balances the gravitational force acting on it. To find the charge per unit area on the plastic sheet, consider: 1. **Electrostatic Force:** This force is due to the electric field (E) produced by the charge density (σ) of the sheet, where \( E = \frac{\sigma}{2 \varepsilon_0} \). 2. **Gravitational Force:** Given by \( F_g = mg \), where \( m = 10.0 \, \text{g} \) and \( g = 9.81 \, \text{m/s}^2 \). 3. **Equilibrium Condition:** \( F_e = F_g \), where \( F_e = qE \), and \( q = -0.700 \, \mu \text{C} \). Using these, you can derive the charge density needed to keep the Styrofoam in equilibrium.
Transcribed Image Text:**Problem 25:** A 10.0-g piece of Styrofoam carries a net charge of -0.700 μC and is suspended in equilibrium above the center of a large, horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet? --- **Explanation:** In this scenario, a piece of Styrofoam with a given net charge is suspended above a plastic sheet due to electrostatic forces. The equilibrium condition implies that the electrostatic force exerted by the charged sheet on the Styrofoam balances the gravitational force acting on it. To find the charge per unit area on the plastic sheet, consider: 1. **Electrostatic Force:** This force is due to the electric field (E) produced by the charge density (σ) of the sheet, where \( E = \frac{\sigma}{2 \varepsilon_0} \). 2. **Gravitational Force:** Given by \( F_g = mg \), where \( m = 10.0 \, \text{g} \) and \( g = 9.81 \, \text{m/s}^2 \). 3. **Equilibrium Condition:** \( F_e = F_g \), where \( F_e = qE \), and \( q = -0.700 \, \mu \text{C} \). Using these, you can derive the charge density needed to keep the Styrofoam in equilibrium.
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