### 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

Solution: As per the given data,

Answered: (b) What If? What is the minimum…

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