### Electric Fields and Point Charges: An Educational Overview#### (a) Electric Field Calculation**Problem:**Three point charges are located on the circumference of a circle of radius \( r \), at the angles shown in the figure below.**Diagram Explanation:**The diagram consists of a circle with three point charges positioned on its circumference:- A charge \( +q \) located at \( 150^\circ \)- A charge \( +q \) located at \( 30^\circ \)- A charge \( -2q \) located at \( 270^\circ \)Each charge is at an equal distance \( r \) from the center of the circle. The coordinate system has the origin at the center of the circle.**Question:**What is the electric field at the center of the circle due to these point charges? (Express your answer in vector form. Use the following as necessary: \( k_e \), \( q \), and \( r \).)**Solution:**The electric field at the center of the circle due to these point charges is given as:\[\vec{E} = \frac{3k_e q}{r^2} (-\hat{j})\]This indicates that the net electric field vector at the center points downward along the negative \( y \)-axis.#### (b) Minimum Electric Field Magnitude**Question:**What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with a minimum separation of \( 8.70^\circ \) between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a).**Answer:**The answer box for this part indicates that further calculations or considerations are needed to find the minimum electric field magnitude and then to express it as a ratio compared to the electric field found in part (a).**Ratio Expression:**\[\frac{E_{\text{minimum}}}{E_{\text{part (a)}}} = \]This part requires following steps to determine the minimum possible electric field:1. Reposition the charges so that the resulting electric field at the center is minimized.2. Ensure that the new positions maintain a minimum separation of \( 8.70^\circ \).3. Calculate the new electric field and determine the ratio to

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(b) What If? What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with minimum separation of 8.70° between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a). Eminimum Epart (a)

(b) What If? What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with minimum separation of 8.70° between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a). Eminimum Epart (a)