Question

Q1 = +2.1µC and is located at (5, 0), Q2 = -8.4µC and is located at...

  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 QB = +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.
    1. Find the force from Q1 on the ball in component form?
    1. Find the force from Q2 on the ball in component form?
    1. Find the force from Q3 on the ball in component form?
    1. What is the magnitude of the net force acting on the ball?
    1. In what direction is the net force on the ball acting? (give an answer as an angle measured CCW from the +x axis)
    1. A fourth charge, Q4 = +5µC, is placed such that the ball is in equilibrium. What must the coordinates of Q4 be?
  1. 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?
  1. 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?
    1. If q=1.2 µC what would the net force on Q1
    1. 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?
  1. 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?
    1. 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?

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