Please answer fast and clearly. How does Gauss\'s law for electrostatics imply t

Question

Please answer fast and clearly.

How does Gauss's law for electrostatics imply that isolated electric charges can exist, white Gauss's law for magnetism implies that they cannot? When an inductor is placed in an electric circuit, consisting of a resistor, a voltage source, and the inductor itself, is it the self or the mutual inductance that enters into the current calculation? Using Gauss's law, explain why the charges inside a conductor have to be on the surface. For a positively charged particle moving in the +x direction, explain how we can deflect the particle upwards using either a magnetic or an electric field Using what we learned in class, Explain how you can generate electric power from a) a hydraulic damn and b) a wind turbine

Explanation / Answer

a) since del*E = rho, thus there can be a net charge density

but since del*B = 0, no net magnetic density so no isolated magnetic ahrge

b) self, since inductor iteracts with iteself

c) since netflux = EA = qenc/e0

since E = 0, q enc = 0, so charges have to be on outside

d) with electric field point field up

with magnetic field point in +y so then, vxB is in the z direction

e) water falls hitting a turbine and spinning it which moves magnets, which cause a change in magnetic flux and thus an emf and thus a current

same idea for wind.

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