Chapter 21: Problem 14
Occasionally, people who gain static charge by shuffling their feet on the carpet will have their hair stand on end. Why does this happen?
Chapter 21: Problem 14
Occasionally, people who gain static charge by shuffling their feet on the carpet will have their hair stand on end. Why does this happen?
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Get started for freeIn general, astronomical objects are not exactly electrically neutral. Suppose the Earth and the Moon each carry a charge of \(-1.00 \cdot 10^{6} \mathrm{C}\) (this is approximately correct; a more precise value is identified in Chapter 22 ). a) Compare the resulting electrostatic repulsion with the gravitational attraction between the Moon and the Earth. Look up any necessary data. b) What effects does this electrostatic force have on the size, shape, and stability of the Moon's orbit around the Earth?
Two equal magnitude negative charges \((-q\) and \(-q)\) are fixed at coordinates \((-d, 0)\) and \((d, 0) .\) A positive charge of the same magnitude, \(q\), and with mass \(m\) is placed at coordinate \((0,0),\) midway between the two negative charges. If the positive charge is moved a distance \(\delta \ll d\) in the positive \(y\) -direction and then released, the resulting motion will be that of a harmonic oscillator-the positive charge will oscillate between coordinates \((0, \delta)\) and \((0,-\delta)\). Find the net force acting on the positive charge when it moves to \((0, \delta)\) and use the binomial expansion \((1+x)^{n} \approx 1+n x,\) for \(x \ll 1,\) to find an expression for the frequency of the resulting oscillation.
A small ball with a mass of \(30.0 \mathrm{~g}\) and a charge of \(-0.200 \mu \mathrm{C}\) is suspended from the ceiling by a string. The ball hangs at a distance of \(5.00 \mathrm{~cm}\) above an insulating floor. If a second small ball with a mass of \(50.0 \mathrm{~g}\) and a charge of \(0.400 \mu \mathrm{C}\) is rolled directly beneath the first ball, will the second ball leave the floor? What is the tension in the string when the second ball is directly beneath the first ball?
In the Bohr model of the hydrogen atom, the electron moves around the one- proton nucleus on circular orbits of well-determined radii, given by \(r_{n}=n^{2} a_{\mathrm{B}}\), where \(n=1,2,3, \ldots\) is an integer that defines the orbit and \(a_{\mathrm{B}}=5.29 \cdot 10^{-11} \mathrm{~m}\) is the radius of the first (minimum) orbit, called the Bohr radius. Calculate the force of electrostatic interaction between the electron and the proton in the hydrogen atom for the first four orbits. Compare the strength of this interaction to the gravitational interaction between the proton and the electron.
A charge \(Q_{1}\) is positioned on the \(x\) -axis at \(x=a\). Where should a charge \(Q_{2}=-4 Q_{1}\) be placed to produce a net electrostatic force of zero on a third charge, \(Q_{3}=Q_{1}\), located at the origin? a) at the origin c) at \(x=-2 a\) b) at \(x=2 a\) d) at \(x=-a\)
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