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Its raining and your trying to decide whether or not to run or walk. If you walk you'll spend longer in the rain, but if you run you'll be running into the rain and potentially get wetter. The rain is falling with a velocity of which has both an x-component as it blows sideways and a y-component as it falls. You move with a velocity of which only has an x-direction. If the rain is falling with a density and you have a top area of (which rain will fall onto) and a sideways area of (which rain will fall onto if it blows sideways or you move sideways into it), find an expression for how wet you would be when traveling a distance d, as a function of your velocity.
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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