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E+M Warmups
Consider a small black ball of radius \(R\) and density \(\rho= 1~\frac{\mbox{g}}{\mbox{cm}^{3}}\) located at a certain distance above the surface of the Sun. For what radius \(R\) in micrometers is the gravitational attraction of the Sun counterbalanced by the radiation force?
Assume that the black ball absorbs all the incident light and that the total power radiated by the Sun is \(P=4\times 10^{26}~\mbox{W}\).
Details and assumptions
The mass of the Sun is \(M_{s}=2\times 10^{30}~\mbox{kg}\). The universal constant of gravitation is \(G=6.67\times 10^{-11}~\text{m}^{3}\text{kg}^{-1} \text{s}^{-2}\) and the speed of light \(c=3\times 10^{8}~\mbox{m/s}\).
by
David Mattingly
Two 1-g beads with charges \(Q_{x}=2~\mu\mbox{C} \) and \(Q_{y}=-3~\mu\mbox{C}\) slide on (without friction) two perpendicular wires (\(x\) and \(y\) axes). The charges are initially located at \((5~\mbox{m},0)\) and \((0,3~\mbox{m})\) and released from rest.
What is the distance in meters between the charges when \(Q_{y}\) crosses the origin \((0,0)\)?
Details and assumptions
\[ k=\frac{1}{4\pi \epsilon_{0}}=9 \times 10^{9} \mbox{N m}^{2}/\mbox{C}^{2}\]
by
David Mattingly
by
David Mattingly
Christmas tree lights can be put together in either series or parallel. Consider 100 Christmas tree lights, each with a resistance of 1\(\Omega\). Let circuit P be all the lights hooked up in parallel to an electrical outlet, and circuit S be all the lights hooked up in series. What is the ratio of the power used in P to the power used in S?
by
David Mattingly
The Hyperloop is a hypothetical new fast transport system between cities, which works by launching pods that carry people through a very low air pressure tunnel. If we model the Hyperloop pod as a hollow metal cylinder with a radius of \(1~\mbox{m}\) and a length of \(10~\mbox{m}\), what is the maximum voltage difference between the sides of the pod in Volts?
Details and assumptions
- The magnetic field at the earth's surface is \(0.5~\mbox{Gauss}\).
- The speed of the pod is \(300~\mbox{m/s}\).
by
David Mattingly