Physics 1220 In-Class Problems: Coulomb's Law and Electric Fields

1. Copper has a density of 8.890 × 10³ kg/m³, an atomic number of 29, and an atomic mass of 63.546 g. Determine the number of electrons per cubic centimetre in a chunk of copper. Atomic number is the number of protons, and hence the number of electrons, in a neutral atom. Atomic mass is the mass of one mole (6.0221 × 10²³) of the particular atoms in question.
2. There are three identical metal spheres, A, B, and C. Sphere A carries a charge of +5q. Sphere B carries a charge of -q. Sphere C carries no charge. Spheres A and B are touched together then separated. Sphere C is then touched to sphere A and separated from it. Lastly, sphere C is touched to sphere B and separated from it. How much charge ends up on sphere C?
3. Where would you put a positive charge of +1 μC in the diagram below so that the net force on it is zero?






4. What is the net force on charge A in each configuration shown below? The distances are r₁ = 12.0 cm and r₂ = 20.0 cm.







5. A charged ball of mass m = 0.265 kg and unknown q is hanging by a light thread from a ceiling. A fixed charge Q = +5.00 μC on an insulated stand is brought close to the unknown charge. As a result, the unknown charge hangs at an angle θ = 38.0° to the vertical as shown in the diagram below. The distance between the two charges is r = 22.0 cm.

(a) What is the sign of the unknown charge? Explain how you know this.
(b) What is the magnitude of the unknown charge?



6. An object has a mass of 215 kg and is located at the surface of the earth (mass = 5.98 × 10²⁴ kg, radius = 6.38 × 10⁶ m). Suppose this object and the earth each have identical charge q. Assuming that the earth's charge is located at the centre of the earth, determine q such that the electrostatic force exactly cancels the gravitational force.
7. Three point charges q₁ = -1.00 μC, q₂ = 2.00 μC, and q₃ = 3.00 μC are placed at the corners of an equilateral triangle of side length L = 0.250 m. Find the magnitude and the direction of the electric field at (a) a point midway between charges q₁ and q₂, and at (b) the centre of the equilateral triangle.






8. The distances on the graph below are in metres.  The charges are Q₁ = –3 μC, Q₂ = 2 μC, and Q₃ = 5 μC. Find the net electric field at the origin.

   

9. Find the net electric field at point A in the diagram below.



10. A small ball of mass m = 0.015 kg is suspended floating in an electric field of magnitude E = 5000 N/C. (a) If the electric field is pointing straight up into the air, what is the charge on the ball? (b) If E points straight down?
11. A ball of mass m = 0.010 kg and charge q is tied by a very light string to the ceiling. The effects of a uniform electric field E = 5000 N/C has caused the charged ball to move to one side so that the string makes an angle of θ = 37° with the vertical. Draw the free body diagram of the floating ball. Determine the magnitude of the charge q. How can you tell the sign (positive or negative) of the charge?

Questions? mike.coombes@kwantlen.ca