The Physics
Opus in profectus

Electric Field

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  1. Sketch the electric field around the following arrangements of "small" charged objects.
    1. an isolated positive charge
    2. an isolated negative charge
    3. two positive charges of equal magnitude
    4. two negative charges of equal magnitude
    5. an electric dipole (one positive and one negative charge of equal magnitude)
  2. sketch-e.pdf
    The diagram below shows the location and charge of two identical small spheres. Find the magnitude and direction of the electric field at the five points indicated with open circles. Use these results and symmetry to find the electric field at as many points as possible without additional calculation. Write your results on or near the points. Sketch the approximate magnitude and direction of the field at these points.

    The setup

  3. Van de Graaff generator
    A charged object will spark spontaneously when the electric field on its surface exceeds 3 × 106 N/C, the dielectric strength of air. This prevents it from acquiring any more charge. A typical Van de Graaff generator for classroom use is probably 75 cm tall and has a collector dome that is 30 cm in diameter.
    1. What maximum charge can a Van de Graaff generator like the one I just described hold?
    2. How many of these Van de Graaff generators would you need to separate one coulomb of charge?
  4. Write something completely different.


  1. What happens to the strength of the electric field at any location in space if the magnitude of the charge used to test the field is…
    1. doubled?
    2. halved?
  2. Sketch the electric field around the following pairs of point charges. Draw continuous field lines and assume the charges are separated by a few centimeters of empty space.
    1. A +3 μC charge on the left and a +1 μC charge on the right.
    2. A +3 μC charge on the left and a −1 μC charge on the right.


  1. The electric field of the Earth is due to the separation of charges between the surface of the Earth and the upper layers of the Earth's atmosphere.
    1. If the direction of the Earth's electric field points down, what is the sign of the charge on the Earth's surface? Explain your answer.
    2. Is the charge on the surface of the Earth due to an excess or a deficit of electrons? Explain your answer.
    3. An estimate of the net charge on the Earth can be made by assuming that all of the charge on the Earth is concentrated at its center. If the electric field on the Earth's surface is 120 N/C, what is the net charge of the Earth?
    4. Calculate the surface area of the Earth.
    5. What is the surface charge density of the Earth in…
      1. coulombs per square meter [C/m2] and
      2. elementary charges per square meter [e/m2].
  2. A charge of −1.0 μC is located on the y-axis 1.0 m from the origin at the coordinates (0,1) while a second charge of +1.0 μC is located on the x-axis 1.0 m from the origin at the coordinates (1,0). Determine the…
    1. magnitude and
    2. direction
    …of the electric field at the origin.
  3. Cartoon representation
    The drawing on the right shows two charged objects, one located at the origin indicated by a solid circle and a second located first at point A and then at point B (indicated by open circles). Points on the grid are separated by one meter. Thus point A is 3 m right and 4 m down relative to the origin and point B is 8 m right and 6 m up relative to the origin. The magnitude of the electrostatic force on the second charge is 20 N when it is located at point A. Determine the magnitude of the electrostatic force when the second charge is moved to point B.
  4. An old fashioned television picture tube (also known as a cathode ray tube or CRT) is about a half meter long and has a potential difference of about 10,000 V between the front and the back. Determine the following quantities inside a typical CRT TV.
    1. the electric field strength
    2. the force on an electron
    3. the acceleration of an electron
    Determine the following quantities for an electron in a typical CRT when it strikes the phosphor coating on the front of the tube.
    1. its velocity
    2. its kinetic energy
    Electrons with this much energy will produce x-rays when stopped abruptly.
    1. Are the x-rays produced by a CRT television a matter for concern? If yes, why? If not, why not?