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Chapter 22: Problem 11
Is the potential at the center of a hollow, uniformly charged spherical shell higher than, lower than, or the same as at the surface?
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A sphere of radius \(R\) carries a nonuniform but spherically symmetric volume charge density that results in an electric field in the sphere given by \(\vec{E}=E_{0}(r / R)^{2} \hat{r},\) where \(E_{0}\) is a constant. Find the potential difference from the sphere's surface to its center.
Measurements of the potential at points on the axis of a charged disk are given in the two tables below, one for measurements made close to the disk and the other for measurements made far away. In both tables \(x\) is the coordinate measured along the disk axis with the origin at the disk center, and the zero of potential is taken at infinity. (a) For each set of data, determine a quantity that, when you plot potential against it, should yield a straight line. Make your plots, establish a best-fit line, and determine its slope. Use your slopes to find (b) the total charge on the disk and (c) the disk radius. (Hint: Consult Example 22.7.) Table 1 $$\begin{array}{|l|l|l|l|l|l|} \hline x(\mathrm{mm}) & 2.0 & 4.0 & 6.0 & 8.0 & 10.0 \\ \hline V(\mathrm{V}) & 900 & 876 & 843 & 820 & 797 \\ \hline \end{array}$$ Table 2 $$\begin{array}{|l|l|l|l|l|l|} \hline x(\mathrm{cm}) & 20 & 30 & 40 & 60 & 100 \\ \hline V(\mathrm{V}) & 165 & 118 & 80 & 58 & 30 \\ \hline \end{array}$$
Points \(A\) and \(B\) lie \(32.0 \mathrm{cm}\) apart on a line extending radially from a point charge \(Q,\) and the potentials at these points are \(V_{A}=362 \mathrm{V}\) and \(V_{B}=146 \mathrm{V} .\) Find \(Q\) and the distance \(r\) between point \(A\) and the charge.
The potential difference between the two sides of an ordinary electric outlet is \(120 \mathrm{V}\). How much energy does an electron gain when it moves from one side to the other?
Two equal but opposite charges form a dipole. Describe the equipotential surface on which \(V=0\)
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