Physics A: Problem Set 3: Electric field

drawing for notes

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)

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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.
3. 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 direction of the electric field at the origin.
4. 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].

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5. The more common unit for the electric field is the volt per meter [V/m].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.

   4. its velocity
   5. its kinetic energy

   Electrons with this much energy will produce x-rays when stopped abruptly.

   6. Are the x-rays produced by a CRT television a matter for concern? If yes, why? If not, why not?