Question

Force Between Two Spheres Two small no conducting spheres have a total positive charge of 1343.0 microc. when paced·01 m apart, the force each exerts on the other s 15.2 N and s repulsive. what s the arge charge on the s ees? Submit Answer Tries of10 What is the (smaller) charge on the other sphere? Submit Answer Tries 0/10 What if the force were attractive? What is the larger charge on one of the spheres? Submit Answer Tries of10 What is the smaller charge on the sphere? Submit Answer Tries 0/10

Answer 1

given

q1 + q2 = 1343 uC

q1 = 1343e-6 - q2

Now,

F = 9e9 * q1q1 / 1.01²

15.2 = 9e9 * q1q1 / 1.01²

1.7228e-9 = q1q2

1.7228e-9 = (1343e-6 - q2)q2

1.7228e-9 = 1343e-6q2 - q2²

- q2² + 1343e-6q2 - 1.7228e-9 = 0

solve this quadratic equation, we have

-1343e-6 +/- sqrt (1.8036e-6 - 6.89e-9) / -2

q2 = -1343e-6 +/- 1.3404e-3 / -2

q2 = 1.3417e-3 C (larger charge) and 1.3e-6 C (smaller charge)

if force was attractive, one of above two will be negative.