1. (2 pts) A charge of -7C is fixed at the origin. A charge of +3C is moved from a position 5cm away from the charge to one 8cm away from the charge.

    (a). Defining the electrical potential energy as zero if infinitely far away from a charge, what are the initial, final, and change in electrical potential energy of the charge?                           Remember to include a plus or minus sign as appropriate.

     (b). How much work is done by the electric force (not the force being used to move the charge!) in this process? Remember to include a plus or minus sign as appropriate. 

• •        1. (2 pts.) Three charges are placed in a plane, with 1μC at x=0 cm, y = 3cm, -2μC at x=6cm, y=0cm, and +4μC at (x,y) = (0cm, 0cm)

           1 μC (0, 3cm)

          4 μC (0cm, 0 cm) -2 μC (6cm, 0cm)

         (a) Find the x and y components of the total electrical force exerted on the 4μC charge.

         (b) Find the magnitude and direction of the total force on the 4μC charge.

    
    

    2. (2 pts) For the charge configuration of Problem 1, find the total electric field due to the set of 3 charges at the point (x,y) = (6cm, 3cm). Supply the answer as:

         (a) The x and y components of the field, and

         (b) The magnitude and direction of the field.

    3. (1 pt) For the above charge configuration, a fourth charge of -4μC is placed at (x,y) = (6cm, 3cm). Find the magnitude and direction of the force on this fourth charge.

    4. (2 pts) Start with the charge configuration of problem 3.

          (a). Find a position and value of a fifth charge that can be placed in such a way that the total force on the fourth charge is zero.

          (b) Is it possible to find a solution for the fifth charge with it lying outside the plane of the other four charges? Why or why not?

    
    

    5.   (1 pt) A pair of charges very close together with dipole moment 1 x 10^-8 C-m pointing in the +z direction is place at the origin.

  
  

  •        What is the approximate electric field due to this dipole at (x,y,z) = (0m, 2m, 0m)?

  6.  (2 pts) Draw the field lines for the following charge configuration:

            +Q -Q

            -Q +Q

  
  

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