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 = 5.50 µC, q2 = 1.17 µC, and q3 = ?2.39 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

3.62 µC,

calculate magnitude and direction of the force on it.

Explanation / Answer

electric field is always directed away from positive charge and towards the negative charge

E = kq/r = K( 5.50 x 10^-6)/ ( 2 x 10^-2)^2 + K (-2.39 x 10^-6)/ ( 3 x10^-2 )^2 - K ( 1.17 x 10^-6)/ ( 1 x 10^-2)^2 = (8.9 x 10^7) ( 1.375 - 0.265 - 1.17) = - 5.34 x 10^ 6 N/m apprx

F= qE = 3.62 x 10^-6 (-5.34 x 10^6) = =- 19.3308 N apprx ( towards right)

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