Discussion Questions
1. A negative charge in an electric field moves from a point where the potential is zero to a point where it is - 100 V. Discuss the energy change and the work done.
2. Imagine a hollow, spherical, positively charged conductor of radius R that is far away from any other bodies. Draw a graph of its potential V, as a function of r out from its center. Discuss your results.
3. With Question 2 in mind, suppose we place a neutral hollow conducting sphere in the vicinity of the charged sphere. Draw a rough graph of the potential along the center line of both spheres and compare it to the previous potential without the neutral conductor. Discuss your results.
4. With Question 3 in mind, suppose we ground the neutral conductor. Describe the potential along the center line. Discuss your results.
13. We know that points infinitely far from all charges are at zero potential and yet, as a practical matter, we take the Earth, which may well be charged, to be at zero potential. How can this inconsistency be resolved?
Problems
1. A tiny sphere carrying a charge of -25 nC is moved 100 cm in an uniform electric field with no acceleration. It goes from a location at a potential of 0 to a point where the potential is 100 V. How much work is done on it by the applied force? What is the significance of the sign of delta W?
3. What voltage should be put across a pair of parallel metal plates 10 cm apart if the field between them is to be 1 V/m?
5. Figure P5 show two hollow concentric metal spheres of radii rho and R. If the inner one is charged with +Q and the outer surface is grounded, what is the potential at any point P outside the larger sphere? Explain your thinking.
7. Two small spheres charges of +30 micro C and -50 micro C are 100 cm apart in air. What is the potential at a point on the center-to-center line midway between them?
10. It is fairly easy to strip the two electrons off a helium atom leaving a a bare nucleus of two neutrons and two protons. That so-called alpha particle is to be accelerated, essentially from rest, up to a KE of 100 keV by having it "fall" through a potential difference. What is the necessary voltage difference?
17. Two horizontal parallel metal plates 10 cm apart in a vacuum chamber are to be used to suspend an electron in "midair." What voltage must be put across the plates?
18. Tiny conducting spheres carrying charges of +60 micro C are fixed at each of the four corners of a square 20 cm on a side. What is the potential at the center? What is the electric field at the center? Assume the medium is a vacuum.
20. Points charges of +300 nC, -700 nC, +500 nC, and -100 nC are located in sequence at the corners of a square 40 cm on a side. Determine the potential at the center of the square.