The figure shows a small sphere of mass 1.5x10-14 kg held in equilibrium between two parallel metal plates by electrostatic and gravitational forces. If the plates are 2.5x10-² m apart and the sphere at P carries a positive charge of magnitude 4.8x10-19 C, what is the magnitude of the electric field between the plates?

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The figure illustrates a small sphere with a mass of \(1.5 \times 10^{-14}\) kg suspended in equilibrium between two parallel metal plates. This equilibrium is maintained by the interplay of electrostatic and gravitational forces. The distance between the plates is \(2.5 \times 10^{-2}\) meters, and the sphere located at point P has a positive charge of \(4.8 \times 10^{-19}\) C. The question posed is: What is the magnitude of the electric field between the plates?

**Diagram:**

- **Negative Plate:** Positioned at the top of the diagram.
- **Positive Plate:** Positioned at the bottom of the diagram.
- **Distance Between Plates:** The plates are separated by a distance of \(2.5 \times 10^{-2}\) m, as indicated by a double-headed arrow.

**Options for the Magnitude of the Electric Field:**

- \(8.4 \times 10^{4}\) N/C
- \(3.1 \times 10^{5}\) N/C
- \(4.8 \times 10^{4}\) N/C
- \(2.2 \times 10^{5}\) N/C

The sphere at point P is shown in equilibrium, indicating that the electric force and the gravitational force are balanced. Determine the correct magnitude of the electric field by analyzing these forces.
Transcribed Image Text:The figure illustrates a small sphere with a mass of \(1.5 \times 10^{-14}\) kg suspended in equilibrium between two parallel metal plates. This equilibrium is maintained by the interplay of electrostatic and gravitational forces. The distance between the plates is \(2.5 \times 10^{-2}\) meters, and the sphere located at point P has a positive charge of \(4.8 \times 10^{-19}\) C. The question posed is: What is the magnitude of the electric field between the plates? **Diagram:** - **Negative Plate:** Positioned at the top of the diagram. - **Positive Plate:** Positioned at the bottom of the diagram. - **Distance Between Plates:** The plates are separated by a distance of \(2.5 \times 10^{-2}\) m, as indicated by a double-headed arrow. **Options for the Magnitude of the Electric Field:** - \(8.4 \times 10^{4}\) N/C - \(3.1 \times 10^{5}\) N/C - \(4.8 \times 10^{4}\) N/C - \(2.2 \times 10^{5}\) N/C The sphere at point P is shown in equilibrium, indicating that the electric force and the gravitational force are balanced. Determine the correct magnitude of the electric field by analyzing these forces.
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