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A small plastic ball of mass m = 2.50 g is suspended by a string of length L = 19.5 cm in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a 8 = 14.0° angle with the vertical as indicated, what the net charge on the ball? HC 10 E=1.00 x10³ N/C L m @

A small plastic ball of mass m = 2.50 g is suspended by a string of length L = 19.5 cm in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a 8 = 14.0° angle with the vertical as indicated, what the net charge on the ball? HC 10 E=1.00 x10³ N/C L m @

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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**Problem Statement:** A small plastic ball of mass \( m = 2.50 \, \text{g} \) is suspended by a string of length \( L = 19.5 \, \text{cm} \) in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a \( \theta = 14.0^\circ \) angle with the vertical as indicated, what is the net charge on the ball? **Diagram Explanation:** 1. **Ball and String Setup:** - The diagram shows a small plastic ball of mass \( m \) suspended by a string of length \( L \), forming an angle \( \theta \) with the vertical. - The string is attached to a fixed point above the ball. 2. **Electric Field:** - A uniform electric field \( E = 1.00 \times 10^3 \, \text{N/C} \) is directed horizontally, from left to right. - The electric field is represented by several parallel arrows pointing horizontally in the positive x-direction. 3. **Coordinate Axes:** - A dashed line represents the vertical, against which the angle \( \theta \) is measured. - The coordinate axes are defined where the vertical axis is the y-axis and the horizontal axis is the x-axis. 4. **Requirements:** - A box is present where the net charge on the ball in microcoulombs (\( \mu \text{C} \)) needs to be calculated. **Note:** This problem, typically found in physics, involves analyzing forces such as tension, weight, and electric force to find the net charge on the ball that results in equilibrium.
Transcribed Image Text:**Problem Statement:** A small plastic ball of mass \( m = 2.50 \, \text{g} \) is suspended by a string of length \( L = 19.5 \, \text{cm} \) in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a \( \theta = 14.0^\circ \) angle with the vertical as indicated, what is the net charge on the ball? **Diagram Explanation:** 1. **Ball and String Setup:** - The diagram shows a small plastic ball of mass \( m \) suspended by a string of length \( L \), forming an angle \( \theta \) with the vertical. - The string is attached to a fixed point above the ball. 2. **Electric Field:** - A uniform electric field \( E = 1.00 \times 10^3 \, \text{N/C} \) is directed horizontally, from left to right. - The electric field is represented by several parallel arrows pointing horizontally in the positive x-direction. 3. **Coordinate Axes:** - A dashed line represents the vertical, against which the angle \( \theta \) is measured. - The coordinate axes are defined where the vertical axis is the y-axis and the horizontal axis is the x-axis. 4. **Requirements:** - A box is present where the net charge on the ball in microcoulombs (\( \mu \text{C} \)) needs to be calculated. **Note:** This problem, typically found in physics, involves analyzing forces such as tension, weight, and electric force to find the net charge on the ball that results in equilibrium.
Expert Solution
Step 1

Given:

Mass m = 2.50 g

Length of string L = 19.5 cm

Angle made by string θ=14.0∘

Electric field  E=1×103 N/C

To find:

Net charge on the ball

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