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The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 120°.
(a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (2, 1, 3).
(b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points toward the origin.
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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