1) The map shows the electric potential at a set of points on a 4 cm grid. (each point is 4 cm apart) Sketch the 50 V, 75 V, and 100 V equipotentials. Determine the E field at A, B, and C.

2) Consider the experience of shuffling across the floor and drawing a spark off your knuckles to a door knob. Remember that the dielectric strength (Emax) of air is 3^.10⁶ V/m. What is your potential relative to the doorknob due to the charge on you? You will need to decide the length of the spark that you can create with static electricity in your personal experience -- no surprise you will all get slightly different answers.

3) Given the maximum E field in the air of 3^.10⁶ V/m what is the maximum amount of charge I can place on a 25 cm diameter metal ball? What is the electric potential of the ball when this charge is placed on it? Consider that as you add more and more charge to the ball the E field at the surface of the ball can't grow above a certain maximum field without causing the air to become a conductor.

4) A metal ball with radius 15 cm is attached by a thin wire to another distance metal ball with radius 3 cm. Charge is placed on the large ball until its potential reaches 4.0 kV. How much charge is on the large ball? How much charge is on the small ball? One characteristic of conductors we talked about is that once the movement of charges has stabalized they must be equipotentials -- what does that have to do with this problem though?

5) To the right is a map of the electric potential on the surface of a human torso. The region marked + is at more positive potential and that labeled - is at more negative potential. The lines are equipotentials. Sketch the E field indicated by the potential map and locate the region of strongest E field. If the separation between equipotentials is 3.0 mV what is the magnitude and direciton of the E field 1 cm (on the drawing) above the - sign?

 

6) Shown below is an equipotential map of the ionosphere of the earth. From the data presented sketch the E field and determine the magnitude and direction of the E field at C and D. Be careful not to confuse the edge of the earth with an equipotential. Based on the data which source charge is larger and why?

 

 

7) The electric potential around a dipole consisting of two charges Q separated by a distance 2a is given by the following expression:

where the axis of the dipole in along the y axis. x and y are measured from the center of the dipole. Find a symbolic expression from which you could calculate the x and y components of the E field anywhere around this dipole. While many of you haven't had vector calc you can still do the necessary differentiation if you just remember that while you take the derivative with respect to x, y is a constant and vica versa. Have fun -- its a derivative problem not an integral one!

8) Time to try a different form of integral problem. In this problem we have a circular rod of insulating material on which a charge of -Q has been uniformly distributed. The radius of the circular rod on which the charge has been distributed is R. What is the Electric Potential at a point a distance b directly above the center of the circle? This is essentially the same setting as problem 11 on the Coulomb homework. Work the same process as you go forward with this problem and all will be well. If nothing else it will give us something to talk about at the problem session.