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It is possible to generate electricity using small variations in the Earth's magnetic field but why haven't we done it? The Earth's field has an average strength of 0.5 Gauss that varies on the order of about 1.0 x 10-5 Gauss/second. How big a single stationary circular loop would you have to construct to generate a voltage equivalent to that of an AA-cell battery (about 1.5 V)? How fast would you have to spin a single circular loop with a radius of 1cm to get the same voltage?
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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