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Chapter 22: Problem 14
The electric potential in a region increases linearly with distance. What can you conclude about the electric field in this region?
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You're sizing a new electric transmission line, and you can save money with thinner wire. The potential difference between the line and the ground, \(60 \mathrm{m}\) below, is \(115 \mathrm{kV}\). The field at the wire surface cannot exceed \(25 \%\) of the 3 -MV/m breakdown field in air. Neglecting charges in the ground itself, what minimum wire diameter do you specify? (Hint. You'll have to do a numerical calculation.)
Show that the result of Example 22.8 approaches the field of a point charge for \(x \gg a\). (Hint: You'll need to apply the binomial approximation from Appendix A to the expression \(1 / \sqrt{x^{2}+a^{2}}\) )
A thin ring of radius \(R\) carries charge \(3 Q\) distributed uniformly over three-fourths of its circumference, and \(-Q\) over the rest. Find the potential at the ring's center.
Two points \(A\) and \(B\) lie \(15 \mathrm{cm}\) apart in a uniform electric field, with the path \(A B\) parallel to the field. If the potential difference \(\Delta V_{A B}\) is \(840 \mathrm{V},\) what's the field strength?
The classical picture of the hydrogen atom has the electron orbiting 0.0529 nm from the proton. What's the electric potential associated with the proton's electric field at this distance?
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