A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of λ, and the cylinder has a net charge per unit length of 2λ. From this information, use Gauss’s law to find (a) the charge per unit length on the inner surface of the cylinder, (b) the charge per unit length on the outer surface of the cylinder, and (c) the electric field outside the cylinder a distance r from the axis.

Consider two infinite planes of charge.  One coincides with the x-y plane and has a charge density of +9.5 x 10-12 C/m2.  The second plane coincides with the y-z plane and has a charge density of -9.5 x 10-12 C/m2.  Calculate the magnitude of electric field, in N/C, at any location that is not on the x-y or y-z planes.        Use ε 0 = 8.9 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)

At what distance along the central axis of a uniformly charged plastic disk of radius R = 0.938 m is the magnitude of the electric field equal to 1/4 times the magnitude of the field at the center of the surface of the disk?

Four charged particles are located at the corners of a square of side length a = 30.0 cm, as shown. The unit charge q =+10.0μC. (a) What is the magnitude and direction of the electric field at the lower left corner?

A conducting sphere of radius r1 = 0.21 m has a total charge of Q = 1.6 μC. A second uncharged conducting sphere of radius r2 = 0.29 m is then connected to the first by a thin conducting wire. The spheres are separated by a very large distance compared to their size. What is the total charge on sphere two, Q2 in coulombs?

2 narrow, flat metal plates are positioned vertically, 20.00 cm. The first plate has a positive charge with charge density σ=+630.0 mC/m2 and a second plate has an equal but opposite negative charge with charge density σ=-6300.0 mC/m2 . There are also two narrow, flat metal plates positioned horizontally, 30.00 cm apart, with the top plate given a negative charge, and the bottom plate given an equal but opposite positive charge, such that the electric potential of the bottom plate is 5.00 V higher than the top plate. A small sphere with a mass of m =64.35 g, and a charge of q =22.00 mC is attached to a narrow, stiff, massless, insulating rod with a length of L= 8.00 cm, which is pivoted at point O, which is 2.000 cm from the second plate. The sphere/rod unit is angled at 5 degrees with horizontal and released from rest. Will the sphere/rod ever hit an angle of 0 degrees with the horizontal? If so, how long will it take to reach that point?

Problem 6:   A conducting sphere of radius r1 = 0.18 m has a total charge of Q = 1.4 μC. A second uncharged conducting sphere of radius r2 = 0.42 m is then connected to the first by a thin conducting wire. The spheres are separated by a very large distance compared to their size. What is the total charge on sphere two, Q2 In coulombs