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(II) A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 21-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26° angle with the vertical (Fig. 16-55), what total charge Q must have been applied to the electroscope? Ignore the mass of the wires. 26° 26° 78 cm 78 cm FIGURE 16-55 Problem 16. 02 을 Olle

(II) A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 21-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26° angle with the vertical (Fig. 16-55), what total charge Q must have been applied to the electroscope? Ignore the mass of the wires. 26° 26° 78 cm 78 cm FIGURE 16-55 Problem 16. 02 을 Olle

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### Example Problem 16: Charge on an Electroscope **Problem Statement:** A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 21-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26° angle with the vertical, what total charge \( Q \) must have been applied to the electroscope? Ignore the mass of the wires. **Figure 16-55 Explanation:** - **Diagram:** - The diagram shows an electroscope with two wires extending from a central point. - Each wire is 78 cm long. - At the ends of the wires, there are small spheres. - The wires form a 26° angle with the vertical on each side. - The spheres at the ends of the wires have an equal charge \( \frac{Q}{2} \). **Solution Outline:** To determine the total charge \( Q \) applied to the electroscope, we should consider the forces acting on the wires. 1. **Electrostatic Force:** The repulsive force between the similarly charged spheres spreads them apart, creating the angle with the vertical. 2. **Gravitational Force:** The weight of each sphere acts directly downwards due to gravity. 3. **Tension in the Wires:** The tension in the wires provides a component to balance both the electrostatic and gravitational forces. ### Detailed Calculation (General Outline): 1. **Force Analysis:** - For each sphere, consider the forces in equilibrium. - The components of the tension in the wire must balance the gravitational force and the horizontal electrostatic repulsive force. 2. **Trigonometric Relationships:** - The vertical component of the tension balances the weight of the sphere. - The horizontal component of the tension balances the electrostatic repulsive force between the charges. 3. **Coulomb's Law:** - Use Coulomb's law \( F = k_e \frac{Q^2}{r^2} \) to relate the force to the charges and the distance between the charges. 4. **Distance Calculation:** - Calculate the distance \( r \) between the charged spheres based on their positions and the given angles. 5. **Combine Results:** - Use simultaneous equations to solve for the unknown total charge \( Q \). This problem
Transcribed Image Text:### Example Problem 16: Charge on an Electroscope **Problem Statement:** A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 21-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26° angle with the vertical, what total charge \( Q \) must have been applied to the electroscope? Ignore the mass of the wires. **Figure 16-55 Explanation:** - **Diagram:** - The diagram shows an electroscope with two wires extending from a central point. - Each wire is 78 cm long. - At the ends of the wires, there are small spheres. - The wires form a 26° angle with the vertical on each side. - The spheres at the ends of the wires have an equal charge \( \frac{Q}{2} \). **Solution Outline:** To determine the total charge \( Q \) applied to the electroscope, we should consider the forces acting on the wires. 1. **Electrostatic Force:** The repulsive force between the similarly charged spheres spreads them apart, creating the angle with the vertical. 2. **Gravitational Force:** The weight of each sphere acts directly downwards due to gravity. 3. **Tension in the Wires:** The tension in the wires provides a component to balance both the electrostatic and gravitational forces. ### Detailed Calculation (General Outline): 1. **Force Analysis:** - For each sphere, consider the forces in equilibrium. - The components of the tension in the wire must balance the gravitational force and the horizontal electrostatic repulsive force. 2. **Trigonometric Relationships:** - The vertical component of the tension balances the weight of the sphere. - The horizontal component of the tension balances the electrostatic repulsive force between the charges. 3. **Coulomb's Law:** - Use Coulomb's law \( F = k_e \frac{Q^2}{r^2} \) to relate the force to the charges and the distance between the charges. 4. **Distance Calculation:** - Calculate the distance \( r \) between the charged spheres based on their positions and the given angles. 5. **Combine Results:** - Use simultaneous equations to solve for the unknown total charge \( Q \). This problem
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