Three charged marbles are glued to a nonconducting surface and are placed in the

Question

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 = 5.55 mu C, q_2 = 1.00 mu C, and q_3 = -1.69 mu C. Marble q_1 is a distance r_1 = 3.00 cm to the left of the marble q_2, while marble q_3 is a distance r_3 = 2.00 cm to the right of the marble q_2, as shown. Calculate the magnitude of the electric field a distance r = 1.00 cm to the left of the center marble. What is the electric field due to each individual marble? How do you find the total or "net" electric field when you have several electric fields? N/C Another marble is placed 1 cm to the left of the middle marble. If this new marble has a charge of -3.65 mu C, calculate magnitude and direction of the force on it.

Explanation / Answer

E = kQ / d^2

At the point in question, the field due to q1 is positive (to the right), due to q2 is negative (to the left) and due to q3 is

positive (to the right). Then

E = (9 x 10^9N·m^2/C^2) * (5.55/(0.02m)^2 - 1/(0.01m)^2 + 1.69/(0.03m)^2) * 1 x 10^-6C

E = 5.177 x 10^7 N/C ........ field at 1 cm left of center marble

For fourth marble:

F = q*E = 3.65 x 10^-6C x 5.177 x 10^7 N/C = 189 N

and the direction is "to the left."

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