## Activity Based Physics Thinking Problems in Electromagnetism: Electrostatics |

1) Two large parallel sheets of charge are separated by a distance d,
small compared to the size of the sheets. The area of each sheet is A.
The distance d is small enough that (a) What is the electrostatic potential difference between the two sheets?
2) Two "infinite" plane sheets of surface charge of density
s = -40 mC/m
4) Sketch qualitatively the pattern of electric field lines created by four equal positive charges placed at the corner of a square. Sketch qualitatively the equipotential surfaces for this configuration. (You only need to draw the field and potentials in the plane of the charge. Hint: Use symmetry!) 5) (a) Suppose that I have a conducting sphere of radius R with a charge q. Show that if I bring a small amount of charge dq from infinity up to the surface of the sphere, that it takes an amount of work dW = Kq dq/R. (b) Suppose I have a conducting sphere of radius R with a total charge Q. Show that the amount of work needed to bring up all the charge on the sphere is equal to the energy stored in the field of the sphere when it is considered as a capacitor. 6) Two copper spheres of radius 1cm are supported on rigid insulating rods so that their centers are a distance 100 cm apart. A charge of 0.1 mC is placed on one of the spheres (a) What is the potential difference between the two spheres?
7) In the figure on the left below is displayed a grid with coordinates
measured in meters. On the grid two charges are placed with their positions
indicated as black circles. We call the charge at the position (1,0) q (a) E
field at the point (x,y) = (-1,1) 8) In the Millikan oil drop experiment, an atomizer (a sprayer with
a fine nozzle) is used to introduce many tiny droplets of oil between two
oppositely charged parallel metal plates. Some of the droplets pick up
one or more excess electrons. The charge on the plates is adjusted so that
the electric force on the excess electrons exactly balances the weight
of the droplet. The idea is to look for a droplet that has the smallest
electric force and assume that it has only one excess electron. This lets
the observer measure the charge on the electron. Suppose we are using an
electric field of 3x104 N/C. The charge on one electron is about 1.6x10 9) Define and discuss what we mean by an electric field. 10) A large sheet of plastic of dimensions LxL is charged with a uniformly distributed charge Q. If we approximate the sheet by an infinite plane, we can calculate the electric field it produces. (a) Assuming we are close enough to the surface to treat the plane as
infinite, in what direction does the E field point when observed a distance
d above the plane? A distance d below the plane? Explain why you chose
the directions you did.
14) A system of electrified objects is arranged with some conductors and some insulators, some being charged, others being neutral. The system is observed at a particular instant in time. In this context, explain what is meant by the electrostatic potential V(r). 15) Three charges q (a) Write an expression for the electric-field arising from these three
charges at an arbitrary point represented by the vector
On the left below is a list of four sets of configurations specifying the value of the charges and a positions at which the E field is to be measured. On the right is a list of twelve possible electric fields represented as x-y components. For each of the four configurations select the E-field components which represent the field that would be found at that position.
18) Gauss's law is usually written as an equation in the form . (a) For this equation, specify what each term in this equation means and how it is to be calculated when doing some specific (but arbitrary - not a special case!) calculation. A long thin cylindrical shell of length L and radius R with L>>R
is uniformly covered with a charge Q. If we look for the field near to
the cylinder somewhere about the middle, we can treat the cylinder as if
it were an infinitely long cylinder. Using this assumption, we can calculate
the magnitude and direction of the field at a point a distance d from the
(b) Select an appropriate Gaussian surface. Explain why you chose it.
19) In the figure on the left below is displayed a grid with coordinates
measured in meters. On the grid two charges are placed with their positions
indicated as black circles. The charge q For each of the three cases described below specify: an arrow corresponding
to the directions of the E field from the middle figure and a set of components
from the list on the right. Each of your answers should consist of a capital
letter and a small letter. (K stands for the Coulomb force constant, often
written 1/4pe (a)
E field at the point (x,y) = (1,-1)
On the left below is a list of 5 sets of configurations specifying the
value of the charges and a positions at which the E field is to be measured.
For ease of calculation, these are represented in terms of the Coulomb
constant K = 1/4pe
23) The next two questions concern general applications of Gauss's Law. Gauss's law states where A is a surface and q 23.1. Which of the following statements are true about the surface A appearing in Gauss's Law? a. The surface A must be a closed surface (must cover a volume).
23.2. Which of the following statements are true about the charge q a. The charge q 24) The next four problems refer to the two figures below. In these figures are shown some representative electric field lines associated with some charges. Both pictures show the same charges and field lines, but they are masked in different ways by imaginary closed surfaces drawn for the purpose of hiding the charges from your view.
25) Consider a spherical charge distribution which has a constant density r from r = 0 out to r = a and is zero beyond. Find the electric field for all values of r, both less than and greater than a. Is there a discontinuous change in the field as we pass the surface of the charge distribution at r = a? Is there a discontinuous change at r = 0? |

These problems written and collected by E. F. Redish. These problems
may be freely used in classrooms. They may be copied and cited in published
work if the *Activity Based Physics Electromagnetism Problems site*
is mentioned and the URL given. Web page created and edited by K. A. Vick.

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Last modified June 21, 2002