As shown in the above figure, the point charges qA=4 C q_A = 4 \text{ C} and qB q_B produce potential V V at the point X, X, which is away from qA q_A by a distance of d d and away from qB q_B by a distance of 2d. 2d. If the point charge qC q_C is away from X X by a distance of d d and the total potential at XX is 3V, -3V, what is the sum of the point charges qA, q_A, qB q_B and qC? q_C?

There are two charged metal spheres, as shown in the above figure. The sphere A A with radius r1=16 cm r_1 =16 \text{ cm} is charged with charge Q1=32 C, Q_1 =32 \text{ C} , and the sphere B B with radius r2=8 cm r_2 =8 \text{ cm} is charged with charge Q2=4 C. Q_2 = 4 \text{ C}. If the two spheres touch each other, what is the final charge of the sphere A? A?

Two identical, equally charged metal spheres AA and BB with radius 3 m 3 \text{ m} repel each other with a force of FAB=5×105 N. F_{AB} = 5 \times 10^{-5} \text{ N}. A third identical, uncharged sphere CC touches A,A, and then is placed at the midpoint of AA and B.B. Determine the magnitude of net electrostatic force on C?C?

Three positively charged particles lie on a straight line. Their charges are q1=4 C,q2=5 Cq_1= 4 \text{ C}, q_2 =5 \text{ C} and q3=16 C,q_3=16 \text{ C}, with positions x1=0,x_1 = 0, x2x_2 and x3=r=24 mx_3 = r = 24 \text{ m}. The equilibrium point is placed between q1 q_1 and q3. q_3.

When q1q_1 and q3q_3 are fixed, and q2q_2 is movable, find the equilibrium point for q2. q_2.

As shown in the above diagram, there are three electrically neutral metal spheres: metal sphere AA with radius rA=4 cm, r_A=4 \text{ cm}, metal sphere BB with radius rB=2 cm r_B = 2 \text{ cm} which is positively charged with charge qB=6.0 C, q_B = 6.0 \text{ C} , and metal sphere C C with radius rC=6 cm r_C = 6 \text{ cm} which is negatively charged with charge qC=10.0 C. q_C = -10.0 \text{ C}. If B B touches A A and then touches C, C, what is the final charge of sphere B? B?


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