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16. (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. वात

16. (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. वात

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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**Problem 16: Analyzing an Electroscope with Charged Spheres** **Problem Statement:** A large electroscope is designed with "leaves" composed of 78-cm long wires, each ending with tiny 21-g spheres. Upon charging, it is observed that nearly all the charge resides on the spheres. When these wires each form a 26° angle with the vertical (refer to Figure 16-55), determine the total charge \( Q \) that must have been applied to the electroscope. Neglect the mass of the wires for this calculation. **Figure 16-55 Description:** The diagram illustrates the setup of the electroscope. Two wires, each 78 cm in length, extend symmetrically away from a central point at the top, diverging to form a V-shape. At the end of each wire is a small sphere, each charged equally such that the electrostatic repulsion causes the wires to make a 26° angle with the vertical axis. The notation \( \frac{Q}{2} \) is marked next to each sphere, indicating that the total charge \( Q \) is evenly distributed between the two spheres. **Calculation Hint:** To solve this problem, one would typically balance the electrostatic force with the gravitational and tension forces acting on each sphere, utilizing principles from electrostatics and mechanics. The forces at play include: 1. **Gravitational force:** acting vertically downwards. 2. **Electrostatic repulsion:** acting horizontally between the spheres. 3. **Tension in the wires:** acting along the wire. By resolving these forces and using trigonometric relations given the angles, one can solve for the charge \( Q \). **Key Concepts:** - **Electrostatic Force (Coulomb's Law):** \( F_e = \frac{k_e \cdot (q_1 \cdot q_2)}{r^2} \) - where \( k_e \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are point charges, and \( r \) is the distance between the charges. - **Gravitational Force:** \( F_g = m \cdot g \) - where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity. - **Trigonometry and Vector Resolution:** - Components of forces
Transcribed Image Text:**Problem 16: Analyzing an Electroscope with Charged Spheres** **Problem Statement:** A large electroscope is designed with "leaves" composed of 78-cm long wires, each ending with tiny 21-g spheres. Upon charging, it is observed that nearly all the charge resides on the spheres. When these wires each form a 26° angle with the vertical (refer to Figure 16-55), determine the total charge \( Q \) that must have been applied to the electroscope. Neglect the mass of the wires for this calculation. **Figure 16-55 Description:** The diagram illustrates the setup of the electroscope. Two wires, each 78 cm in length, extend symmetrically away from a central point at the top, diverging to form a V-shape. At the end of each wire is a small sphere, each charged equally such that the electrostatic repulsion causes the wires to make a 26° angle with the vertical axis. The notation \( \frac{Q}{2} \) is marked next to each sphere, indicating that the total charge \( Q \) is evenly distributed between the two spheres. **Calculation Hint:** To solve this problem, one would typically balance the electrostatic force with the gravitational and tension forces acting on each sphere, utilizing principles from electrostatics and mechanics. The forces at play include: 1. **Gravitational force:** acting vertically downwards. 2. **Electrostatic repulsion:** acting horizontally between the spheres. 3. **Tension in the wires:** acting along the wire. By resolving these forces and using trigonometric relations given the angles, one can solve for the charge \( Q \). **Key Concepts:** - **Electrostatic Force (Coulomb's Law):** \( F_e = \frac{k_e \cdot (q_1 \cdot q_2)}{r^2} \) - where \( k_e \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are point charges, and \( r \) is the distance between the charges. - **Gravitational Force:** \( F_g = m \cdot g \) - where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity. - **Trigonometry and Vector Resolution:** - Components of forces
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