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 = 6.25 µC, q2 = 1.44 µC, and q3 = 2.41 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.

Another marble is placed 1 cm to the left of the middle marble. If this new marble has a charge of

3.54 µC,

calculate magnitude and direction of the force on it.

Explanation / Answer

Electric field is given by:

E = kQ/R^2

net electric field at observation point will be:

Enet = E1 - E2 + E3

Enet = kq1/r1^2 - kq2/r2^2 + kq3/r3^2

Using given values:

Enet = 9*10^9*[6.25*10^-6/0.02^2 - 1.44*10^-6/0.01^2 + 2.41*10^-6/0.03^2]

Enet = 35.125*10^6 N/C

B.

Net force on charge at observation point will be:

Fnet = q*Enet

Fnet = 3.54*10^-6*35.125*10^6

Fnet = 124.34 N

Direction will be towards +ve-x-axis.

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