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Electrostatic clamps are used for holding workpieces while they are being machined, for holding silicon wafers during electron beam microfabrication, etc. They comprise an insulated conducting plate maintained at a potential of several thousand volts covered with a thin insulating sheet. The workpiece or the wafer rests on the sheet and is grounded. It is advisable to apply a film of oil to the sheet to prevent sparking.
One particular type operates at 3000 volts and has a holding power of 2 atmospheres (2 x 10^5 pascals). If the insulator is Mylar (relative permittivity = 3.2), what is its thickness?
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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