**Electric Field and Potential Energy Calculation**A uniform electric field of magnitude \(250 \, \text{V/m}\) is directed in the positive \(x\)-direction. A \(+10.0 \, \mu\text{C}\) charge moves from the origin to the point \((x, y) = (20.0 \, \text{cm}, 50.0 \, \text{cm})\).**Questions:**a) What is the change in the potential energy of the charge-field system?b) Through what potential difference does the charge move?---**Explanation of the Problem:**To solve these questions, we need to understand the relationship between electric fields, potential energy, and potential difference. The concepts involved include:- The work done by the electric field,- The potential difference between two points,- The relationship between potential difference and change in potential energy.Let's address each part separately with the relevant equations and concepts.**Graph/Diagram Explanation (if any):**There are no graphs or diagrams provided with this problem. The problem is described using the coordinates on a plane and indicating the direction of the electric field. **Key Formulas and Principles:**1. The electric potential difference \(V\) is related to the electric field \(E\) by the equation \( V = E \cdot d \), where \(d\) is the distance moved in the direction of the field.2. The change in potential energy \( \Delta U \) of a charge \( q \) moving through a potential difference \( V \) is given by \( \Delta U = q \cdot V \).**Navigating the Solution:**1. Look at the components of the movement: only the \( x \)-component affects the potential difference since the electric field is in the \( x \)-direction.2. Calculate the \( x \)-component of the displacement.3. Determine the potential difference.4. Find the change in potential energy using the charge value and the calculated potential difference.By carefully following these steps, one can determine both the potential energy change and the potential difference experienced by the charge.

Answered: Image /qna-images/answer/e58a016c-5122-4ce1-9c7f-a3f671f70788.jpg

uniform electric field of magnitude 200 V/m is directed in the positive x direction A +10 oye charge moves from the origin to the point (x, y) = (20.0cm 50.0cm) What is the change in the potential energy of the change fiel system 5) Through what potential difference does the Charge move?

uniform electric field of magnitude 200 V/m is directed in the positive x direction A +10 oye charge moves from the origin to the point (x, y) = (20.0cm 50.0cm) What is the change in the potential energy of the change fiel system 5) Through what potential difference does the Charge move?

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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