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

Question

4. 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 = 1.91 µC, and q3 = ?2.26 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 3.73 µC,

calculate magnitude and direction of the force on it.

magnitude _____________________N

direction _____________________

Explanation / Answer

E = kQ / d²
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 = 8.99e9N·m²/C² * (5.50/(0.02m)² - 1.91/(0.01m)² + 2.26/(0.03m)²) * 1e-6C
E = 2.552e7 N/C field at 1 cm left of center marble

For fourth marble:
F = q*E = 3.73e-6C * 2.552e7N/C = 95.18 N
and the direction is "to the right."

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