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How many electrons must be removed from an electrically neutral silver dollar to give it a charge of +3.8 C? 2. How many electrons would be required to have a total charge of 1.00 C? 3. Two point charges are separated by 10.0 cm. If one charge is +20.0 C and the other is –6.00 C, what is the force between them? 4. Determine the electrostatic force of attraction between a proton and a electron that are separated by a distance of 5.0 x 102 nm. 5. Two identical point charges are 3.00 cm apart. Find the charge on each of them if the force of repulsion is 4.00 x 10–7 N. 6. Two identical point charges are separated by a distance of 3.0 cm and they repel each other with a force of 4.0 x 10–5 N. What is the new force if the distance between the point charges is doubled? 7. An electric force of 2.5 x 10–4 N acts between two small, equally charged spheres which are 2.0 cm apart. Calculate the force acting between the spheres if the charge on one sphere is doubled and the spheres move to a 5.0 cm separation. 8. Three particles are placed on a straight line. The left particle has a charge of +4.6 x 10-6 C, the middle particle has a charge of –2.3 x 10-6 C, and the right particle has a charge of –2.3 x 10-6 C. The particle on the left is 12 cm from the middle particle and the right particle is 24 cm from the middle particle. Find the total force on the middle particle. 9. Three charges are located on a straight line. A charge of +7.5 C is 0.4 cm from a –4.0 C charge. The –4.0 C charge is in turn 0.6 cm away from a +9.0 C charge. What is the net electric force on the middle (-4.0 C) charge? 10. Three charges are located in an equilateral triangle with sides of 0.5 m. The charge located at the top is +3.5C while the two bottom charges are +5.0 C and –5.0 C. What is the net electric force (magnitude and direction) acting on the top charge?

Question

How many electrons must be removed from an electrically neutral silver dollar to give it a charge of +3.8 C? 2. How many electrons would be required to have a total charge of 1.00 C? 3. Two point charges are separated by 10.0 cm. If one charge is +20.0 C and the other is –6.00 C, what is the force between them? 4. Determine the electrostatic force of attraction between a proton and a electron that are separated by a distance of 5.0 x 102 nm.

  1. Two identical point charges are 3.00 cm apart. Find the charge on each of them if the force of repulsion is 4.00 x 10–7 N.
  2. Two identical point charges are separated by a distance of 3.0 cm and they repel each other with a force of 4.0 x 10–5 N. What is the new force if the distance between the point charges is doubled?
  3. An electric force of 2.5 x 10–4 N acts between two small, equally charged spheres which are 2.0 cm apart. Calculate the force acting between the spheres if the charge on one sphere is doubled and the spheres move to a 5.0 cm separation.
  4. Three particles are placed on a straight line. The left particle has a charge of +4.6 x 10-6 C, the middle particle has a charge of –2.3 x 10-6 C, and the right particle has a charge of –2.3 x 10-6 C. The particle on the left is 12 cm from the middle particle and the right particle is 24 cm from the middle particle. Find the total force on the middle particle.
  5. Three charges are located on a straight line. A charge of +7.5 C is 0.4 cm from a –4.0 C charge. The –4.0 C charge is in turn 0.6 cm away from a +9.0 C charge. What is the net electric force on the middle (-4.0 C) charge?
  6. Three charges are located in an equilateral triangle with sides of 0.5 m. The charge located at the top is +3.5C while the two bottom charges are +5.0 C and –5.0 C. What is the net electric force (magnitude and direction) acting on the top charge?
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Solution

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  1. The charge of an electron is -1.6 x 10^-19 C. To find the number of electrons, we divide the total charge by the charge of one electron. So, 3.8 x 10^-6 C / 1.6 x 10^-19 C/electron = 2.375 x 10^13 electrons.

  2. Using the same method as above, 1.00 C / 1.6 x 10^-19 C/electron = 6.25 x 10^18 electrons.

  3. The force between two charges can be calculated using Coulomb's Law: F = k * q1 * q2 / r^2, where k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them. So, F = 8.99 x 10^9 N m^2/C^2 * 20 x 10^-6 C * 6 x 10^-6 C / (0.1 m)^2 = 0.10788 N.

  4. The force between a proton and an electron can also be calculated using Coulomb's Law. The charge of a proton is +1.6 x 10^-19 C and the charge of an electron is -1.6 x 10^-19 C. The distance is 5.0 x 10^2 nm = 5.0 x 10^-7 m. So, F = 8.99 x 10^9 N m^2/C^2 * 1.6 x 10^-19 C * 1.6 x 10^-19 C / (5.0 x 10^-7 m)^2 = 9.2 x 10^-9 N.

  5. This question requires the use of Coulomb's Law in a slightly different form: q = sqrt(F * r^2 / k), where F is the force, r is the distance, and k is Coulomb's constant. So, q = sqrt(4.00 x 10^-7 N * (0.03 m)^2 / 8.99 x 10^9 N m^2/C^2) = 2.0 x 10^-6 C.

  6. According to Coulomb's Law, the force between two charges is inversely proportional to the square of the distance between them. So, if the distance is doubled, the force will be quartered. Therefore, the new force is 4.0 x 10^-5 N / 4 = 1.0 x 10^-5 N.

  7. If the charge on one sphere is doubled, the force will be doubled. If the distance is increased from 2.0 cm to 5.0 cm, the force will be reduced by a factor of (2.0/5.0)^2 = 0.16. Therefore, the new force is 2.5 x 10^-4 N * 2 * 0.16 = 8.0 x 10^-5 N.

  8. & 9. These questions require the use of the principle of superposition, which states that the total force on a charge is the vector sum of the forces exerted on it by the other charges. This involves calculating the force between each pair of charges and then adding the forces vectorially.

  9. This question also requires the use of the principle of superposition, but in a slightly more complex geometry. The forces exerted by the two bottom charges on the top charge must be calculated separately and then added vectorially. The direction of each force is along the line joining the charges, and the magnitude is given by Coulomb's Law.

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