The figure shows a graph of electric potential (V) versus position (x), illustrating a system with three key points: A, B, and C. The potential values and specific x-coordinates are given to find the x-component of the electric field at these points.**Graph Details:**- **Axes:** - The vertical axis represents the electric potential (V) with a labeled value \( V_0 \). - The horizontal axis represents the position (x).- **Points:** - **A**: Located at \( x_1 \) where the potential is \( V_0 \). - **B**: Between \( x_1 \) and \( x_2 \) where the potential remains constant at \( V_0 \). - **C**: At \( x_3 \) where the potential drops to zero.**x-Coordinates and Potential:**- \( x_1 = 25 \, \text{cm} \)- \( x_2 = 100 \, \text{cm} \)- \( x_3 = 150 \, \text{cm} \)- \( V_0 = 12 \, \text{V} \)**Calculation of the Electric Field (E):**The electric field is calculated as the negative gradient (slope) of the potential vs. position graph.- **E-field at point A (\( E_A \)):** \( E_A = -\frac{dV}{dx} \) over the segment 0 to \( x_1 \) - Computed value: \( -48 \, \text{N/C} \) (incorrect value indicated with red 'X')- **E-field at point B (\( E_B \)):** No change in potential between \( x_1 \) and \( x_2 \), so \( E_B = 0 \, \text{N/C} \)- **E-field at point C (\( E_C \)):** \( E_C = -\frac{dV}{dx} \) over the segment \( x_2 \) to \( x_3 \) - Computed value: \( -24 \, \text{N/C} \)This educational example demonstrates how to derive electric field components from a potential vs. position graph. A particle of mass 5 g and charge 21.5 µC is moving in an electric potential field\[ V(x, y) = c_1 \cdot x - c_2 \cdot y^2 + c_3 \cdot y \cdot x^2, \]where \( c_1 = 85 \, \text{V/m}, \, c_2 = 10 \, \text{V/m}^2, \) and \( c_3 = 55 \, \text{V/m}^3. \) Find the electric field acting on the particle as a function of its position. Use V/m and meters for the units, but do not put them explicitly in \(\mathbf{E}(x, y)\).- The x-component of the E-field, \( E_x(x,y) = -55 \) V/m.- The y-component of the E-field, \( E_y(x,y) = 20 \) V/m.What is the magnitude of the particle's acceleration at \( x = 1 \, \text{m} \) and \( y = -0.5 \, \text{m} \)?- The acceleration, \( a = 0.3077 \) \(\text{m/s}^2\).

We know the x-component of the electric field, Ex=-∂V∂x⇒Ex=-∆V∆x This slope of line in graph beween…

Answered: The electric potential of a system is…

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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