Question

1. Q₁ = +2.1µC and is located at (5, 0), Q₂ = -8.4µC and is located at (0, -7), and Q₃ = +6.5 µC and is located at (-8, 6). A ball with a charge of Q_B = +4.2µC is placed at the origin (0,0). (units of distance measured in meters)
   1. Sketch the setup and make an FBD for the ball.
2. 2. Find the force from Q₁ on the ball in component form?
3. 3. Find the force from Q₂ on the ball in component form?
4. 4. Find the force from Q₃ on the ball in component form?
5. 5. What is the magnitude of the net force acting on the ball?
6. 6. In what direction is the net force on the ball acting? (give an answer as an angle measured CCW from the +x axis)
7. 7. A fourth charge, Q₄ = +5µC, is placed such that the ball is in equilibrium. What must the coordinates of Q₄ be?

2. A 15kg block, with charge Q₁ = +2mC, is suspended in equilibrium d meters directly above a second charge, Q₂ = +5µC, in the earth’s gravity (g = 9.81m/s²). (assume constant gravity)

1. Draw and Label the Free Body Diagram of Q₁ in the space below.
2. What is the magnitude and direction of the force of gravity on Q₁?
3. What is the magnitude and direction of the electric force from Q₂ on Q₁?
4. In what directions (if any) is this configuration stable? In which directions (if any) is this configuration unstable? (Hint – think about how the forces on Q₁ change when perturbed)
5. Find the length of d, the distance between Q₁ and Q₂.
6. The charge on Q₁ is doubled, find the new distance between Q₁ and Q₂. What if the charge on Q₁ was halved instead?

3. Four charges are located along the x-axis with Q₀ at x=0, Q₁ at x=1 m, Q₂ at x=2 m, and Q₃ at x=3 m.
   1. If Q₀=16q, Q₂=4q, and Q₃=2q what must the charge of Q₁ be, in terms of q, for the net force on Q₂ to be zero?
4. 2. If q=1.2 µC what would the net force on Q₁
5. 3. A fourth charge, Q₄= +24 µC, is placed along the x-axis. Where must Q₄ be located if the net force on Q₁ is now zero?

4. Four charges of equal magnitude, q = +2.0 µC, are placed at the corners of a square with a side length of 4 meters located in the xy-plane.
   1. A small ball of known charge +3 µC and an unknown mass is placed 2 meters above the center of the square, what is the total force on the ball from the charges?
5. 2. If the ball is in equilibrium where it was placed and we assume standard earth gravity, 9.8 m/s², what must the mass of the ball be?

Answer 1