The charges on three identical metal spheres are -17.4 ? C, 5.80 ? C, and 2.90 ?
ID: 1423938 • Letter: T
Question
The charges on three identical metal spheres are -17.4 ?C, 5.80 ?C, and 2.90 ?C. The spheres are brought together so they simultaneously touch each other. They are then separated and placed on the x and y axes, as shown in the figure. Treat the spheres as if they were particles. What is the net force ((a) magnitude and (b) direction) exerted on the sphere at the origin? Express the direction as an angle in the range (-180°, 180°] with respect to the positive x-axis direction.
+V 42 2.50 mm 41 43 2.50 mmExplanation / Answer
The charges will equalize so they balance
total charge of the 3 spheres together is -8.7 uC
when q1 touches q2 the net charge between them is -11.6 uC so -5.8 uC stays on q1 and -5.8 uC on q2.
when you touch q1 to q3
q1 has -5.8 uC and q3 has 2.9 uC so total is -2.9 uC that means q1 will have -1.45 uC and q3 will gain -1.45 uC.
Net force on q1due to q2 and q3 is F
F1 = kq1q2/r^2 = 0.012 N
F2 = kq1q3/r^2 = 0.003 N
F = (F1^2+F2^2) = 0.0123N
Direction of the force with x axis
= tan^-1(F1/F2) = 76°
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