Electric Current

1. A battery with 12-V emf has a terminal voltage of 11.4 V. When it delivers a delivers a current of 20 A to the starter of a car. What is the internal resistance r of the battery? A) how much emf is delivered but the battery above when it delivers a current of 20 A? (b) how much of this power is delivered to the starter? (c) by how much does the chemical energy of the battery decrease when it delivers a current of 20 A to the starter for 3 min? (d) how much heat is developed in the battery when it delivers a current of 20 A for 3 min?

Point charge above a conducting plate

A point charge Q lies at a distance D above a large grounded conducting plate. a) Calculate the surface charge density induced on the plate as a function of the radius r from the foot of the perpendicular drawn from the charge. b) Show that the total induced charge is -Q.

Field of a charge inside a hollow conducting sphere

(See attached file for full problem description) A hollow grounded conducting sphere of radius a contains a point charge Q at the radius b as shown in the figure (see attachment) a) Show that the field inside the sphere is the same as if there were no sphere and, instead, a charge Q’ = -(a/b)Q at D = (a/b)a. You can prove this by showing that the V of Q plus Q’ is uniform over the surface of the sphere. b) Calculate the force of attraction. c) Calculate the surface charge density on the inside surface of the conducting sphere.

Gradient, divergence and Laplacian in spherical coordinates.

See attached file.

Electrostatic Clamps

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?