Coulomb S Law, Electric Field, Charge Motion, General Problems

APHY112 Exercises

Coulomb’s Law, Electric Field, charge motion, general problems

Useful info:

1. Charged spheres moved. Two charged spheres are 15.59 cm apart. When they are moved, the force on each of them is found to have been tripled. How far apart are they now?

2. Electrons in water. What is the total charge of all the electrons in 1 kg of water?

3. Charges in a triangle. Three charged particles are placed at the corners of an equilateral triangle of side 120 m (see Fig.1). Calculate the magnitude and direction of the net force on each charge due to the two.

4. Charged spheres hung. Two identical spheres of mass m are hung from silk threads of length L, as shown in Fig. 2. Each sphere has the same charge q. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Show that if the angleθis small, the equilibrium separation d between the spheres is . (Hint: if θ is small, then )

5. Zero electric field. Two unknown point charges are separated by distance L. At a point on the line joining them, with distance L/3 from Q1 to Q2, the electric field is zero. What is the ratio Q1/Q2?

6.Proton in electric field. A uniform electric field exists in the region between two oppositely charged parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.6 cm distant from the first, in a time interval of . Find i) the magnitude of the electric field and ii) the speed of the proton when it strikes the negatively charged plate.

7. Charged sphere in equilibrium. A small, 2 g plastic sphere is suspended by a L=20 cm longstring in a uniform electric field E = 1000 N/C as shown in Fig. 3. If the sphere is in equilibrium when the string makesa θ =15.° angle with the vertical, what is the net charge on the sphere?

8.Spheres in electric field.Two small spheres, each of mass 2 g, are suspended by

light strings L=10 cm in length (Fig. 4). A uniformelectric field is applied in the x direction. The sphereshave charges equal to -50 nC and +50nC. Determine the electric field that enables thespheres to be in equilibrium at an angle of θ = 10°.

9. Proton in electric field.A proton accelerates from rest in a uniform electric field

of 640 N/C. At some later time, its speed is (i) Find the acceleration of the proton. (ii) Howlong does it take the proton to reach this speed? (iii) Howfar has it moved in this time? (iv) What is its kinetic energyat this time?