(Solved): Three charged marbles are glued to a nonconducting surface and are placed in the diagram as shown. ...

Three charged marbles are glued to a nonconducting surface and are placed in the diagram as shown. The charges of each marble are \( q_{1}=6.40 \mu \mathrm{C}, q_{2}=1.33 \mu \mathrm{C} \), and \( q_{3}=-1.95 \mu \mathrm{C} \). Marble \( q_{1} \) is a distance \( r_{1}=3.00 \mathrm{~cm} \) to the left of the marble \( q_{2} \), while marble \( q_{3} \) is a distance \( r_{3}=2.00 \mathrm{~cm} \) to the right of the marble \( q_{2} \), as shown. Calculate the magnitude of the electric field a distance \( r=1.00 \mathrm{~cm} \) to the left of the center marble. \( \mathrm{N} / \mathrm{C} \) Another marble is placed \( 1 \mathrm{~cm} \) to the left of the middle marble. If this new marble has a charge of \( -3.59 \mu \mathrm{C} \), calculate magnitude and direction of the force on it. magnitude direction