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How much work does it take to move an electron 7.0 m at an angle of 30.0° to the x-axis, in the presence of a uniform electric field E = 5.0 N/C in the x-axis?

How much work does it take to move an electron 7.0 m at an angle of 30.0° to the x-axis, in the presence of a uniform electric field E = 5.0 N/C in the x-axis?

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
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Question: Calculating Work Done on an Electron in an Electric Field** How much work does it take to move an electron 7.0 m at an angle of 30.0° to the x-axis, in the presence of a uniform electric field \( E = 5.0 \, \text{N/C} \) in the x-axis? --- **Explanation:** To solve this problem, we'll consider the following steps: 1. **Components of Displacement**: - The displacement vector of the electron can be broken down into components along the x and y axes. - \( d_x = 7.0 \, \text{m} \times \cos(30.0^\circ) \) - \( d_y = 7.0 \, \text{m} \times \sin(30.0^\circ) \) 2. **Force on the Electron**: - The force acting on the electron due to the electric field is given by \( F = qE \), where \( q = -1.6 \times 10^{-19} \, \text{C} \) (charge of the electron). 3. **Work Done Calculation**: - Work done \( W \) is calculated as the dot product of the force and the displacement in the direction of the force. - Since the electric field is along the x-axis, work done is \( W = F \cdot d_x \). By analyzing these steps, you can compute the work done to move an electron under these specified conditions.
Transcribed Image Text:**Question: Calculating Work Done on an Electron in an Electric Field** How much work does it take to move an electron 7.0 m at an angle of 30.0° to the x-axis, in the presence of a uniform electric field \( E = 5.0 \, \text{N/C} \) in the x-axis? --- **Explanation:** To solve this problem, we'll consider the following steps: 1. **Components of Displacement**: - The displacement vector of the electron can be broken down into components along the x and y axes. - \( d_x = 7.0 \, \text{m} \times \cos(30.0^\circ) \) - \( d_y = 7.0 \, \text{m} \times \sin(30.0^\circ) \) 2. **Force on the Electron**: - The force acting on the electron due to the electric field is given by \( F = qE \), where \( q = -1.6 \times 10^{-19} \, \text{C} \) (charge of the electron). 3. **Work Done Calculation**: - Work done \( W \) is calculated as the dot product of the force and the displacement in the direction of the force. - Since the electric field is along the x-axis, work done is \( W = F \cdot d_x \). By analyzing these steps, you can compute the work done to move an electron under these specified conditions.
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