Consider the following distribution of charges: two +1 charges are placed at opposite corners, A and C, of a 1 cm square. A negative charge Q of -4 is put in corner B.

(b) The electric field at D has 3 contributions. Those due to charges A and C are both repulsive, and give a vector sum pointing in direction d. The contribution due to charge B is attractive, and points in direction b. The net electric field is the vector sum of both contributions, with its direction depending on the magnitudes of the attraction along b and repulsion along d. The attractive field along b due to charge B has magnitude . The repulsive field is the sum of vectors due to charges A and C, each with magnitude . Thus there is no way that the two repulsive forces, pointing in perpendicular directions, can sum to a contribution along d which is large enough to overcome the greater attractive field along b. Thus the net electric field points along b.

1. Which of the following is an accurate representation of the electric field lines of this configuration? (Circle the appropriate letter.)

   

   (c) Field lines exit positive charges, and enter negative ones. The number of field lines entering or exiting a charge must be proportional to its charge; thus if 2 field lines exit each charge, then 8 field lines must enter the charge. (c) satisfies both these criteria.

2. The electric potential at D is J/C. A 1 test charge is moved from spatial infinity (where V=0) to D.
   
   1. Is positive work done BY or AGAINST the electric force in moving the charge to D?

      BY. Positive work done by the electric force reduces the electric potential energy (it transfers potential energy to kinetic energy). Here the electric potential decreases, so the electric potential energy of our positive test charge decreases, as we move from spatial infinity to D. Thus positive work is done by the electric force. The opposite, negative work is done against it.

   2. What is the magnitude of this work done?

      The work done by the electric force gives the decrease in the test charge's electric potential energy:

      

3. For this question, allow the charge Q at corner B to vary, while the charges at A and C remain +1 . For what value of the charge Q is the electric potential at corner D zero?

   The electric potential at point D is the sum of (scalar) contributions from charges A, B, and C. Charges A and C contribute

   

   Thus, to obtain zero potential at D, charge B must contribute the opposite potential

   

   Solving for Q gives

   

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