Calculate the potential energy of a system of two small

Question

Question 1- A small metal sphere, carrying a net charge of q₁ = -2.50 µC, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q₂ = -7.60 µC and mass 1.70g, is projected toward q₁. When the two spheres are 0.800 in apart, q₂ is moving toward q₁ with speed 22.0 m/s (Figure). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

Part A: What is the speed of q₂ when the spheres are 0.420m apart?

Part B: How close does q₂ get to q₁?

Question 2- In the diagram below there are two charges of +q and -q and six points (a through f) at various distances from the two charges. You will be asked to rank changes in the electric potential along paths between pairs of points.

Part A: Using the diagram to the left, rank each of the given paths on the basis of the change in electric potential. Rank the largest-magnitude positive change (increase in electric potential) as largest and the largest-magnitude negative change (decrease in electric potential) as smallest.

Question 3-

Part A: Calculate the potential energy of a system of two small spheres, one carrying a charge of 2.50 µC and the other a charge of -3.50 µC, with their centers separated by a distance of 0.270m. Assume zero potential energy when the charges are infinitely separated.

Part B: Suppose that one of the spheres is held in place and the other sphere, which has a mass of 2.30g, is shot away from it. What minimum initial speed would the moving sphere need in order to escape completely from the attraction of the fixed sphere? (To escape, the moving sphere would have to reach a velocity of zero when it was infinitely distant from the fixed sphere.)

Question 4- A particle with charge 4.80 x 10^-19C is placed on the x axis in a region where the electric potential due to other charges increases in the +x direction but does not change in the y or z direction.

Part A: The particle, initially at rest, is acted upon only by the electric force and moves from point a to point b along the x axis, increasing its kinetic energy by 8.00 x 10^-19 J. In what direction and through what potential difference V_b - V_a does the particle move?

Part B: If the particle moves from point b to point c in the y direction, what is the change in its potemtial energy, U_c - U_b?

Question 5- Three equal point charges, each with charge 2.00 µC, are placed at the vertices of an equilateral triangle whose sides are of length 0.350m. What is the electric potential energy U of the system? (Take as zero the potential energy of the three charges when they are infinitely far apart.)

Question 6: Charge Q = + 5.00 µC is distributed uniformly over the volume of an insulating sphere that has radius R = 3.00 cm.

Part A: What is the potential difference between the center of the sphere and the surface of the sphere?