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 q1 = 6.60 µC, q2 = 1.18 µC, and q3 = 2.22 µC. Marble q1 is a distance r1 = 3.00 cm to the left of the marble q2, while marble q3 is a distance r3 = 2.00 cm to the right of the marble q2, as shown. Calculate the magnitude of the electric field a distance r' = 1.00 cm to the left of the center marble

______ N/C

Another marble is placed 1 cm to the left of the middle marble. If this new marble has a charge of 3.74 µC, calculate magnitude and direction of the force on it.

Explanation / Answer

Electic field due to q1 is E1 = k*q1/x1^2 = (9*10^9*6.6*10^-6)/(0.03-0.01)^2 = 1.48*10^8 N/C towards q2

Field due to q2 is E2 = k*q2/x2^2 = (9*10^9*1.18*10^-6)/(0.01^2) = 1.062*10^8 N/C towards q1

Field due to q3 is E3 = k*q3/x3^2 = (9*10^9*2.22*10^-6)/(0.03^2) = 0.222*10^8 N/c towards q3

then net field is Enet = (1.48-1.062+0.222)*10^8 = 0.64*10^8 N/C = 6.4*10^7 N/C along +X-axis

force on new marble is F = q*E = 3.74*10^-6*6.4*10^7 = 239.4 N

direction is right

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