4. complete each of the following parts and show your work: a.) draw the electric field around a +2.0 × 10–5 c point source charge. draw the field lines and indicate their direction. draw two different equipotential lines. b.) calculate the force between a +5 µc test point charge and this source charge at a distance of 2.00 cm. (µc = 1.0 × 10–6 c) c.) if the test charge were moved closer to the source charge, would the change in its potential energy be positive, negative or zero? explain.

(a) the electric field generated by a single point charge is radial, and its direction is determined by the sign of the source charge. In particular, when the source charge is positive as in this example, the field lines are directed away from the charge (see attached figure).

(b) The electric field strength at distance r from the source charge is given by

where ke is the Coulomb's constant and Q is the source charge. In our problem, the distance is r=2.00 cm=0.02 m, so the electric field at that point is


The force experienced by the test charge in this electric field is equal to

where  is our test charge. Substituting, we find that the force is equal to


(c) The electric potential at a distance r from the source (positive) charge is given by

and the electric potential energy of a test charge q at distance r from the source charge is

We can see that when the test charge q is moved closer to the source Q, the distance r decreases, and so the potential energy U of the charge increases. So, the change in potential energy is positive.

Arise 8 run 1 this means go 8 up and 1 across, which is steepest