Conducting spheres, electric potential, charge density

Please show all work and show all equations used and diagrams.

1) Two conducting spheres are far apart. The smaller sphere carries a total charge of 6*10^-8C. The larger sphere has a radius that is twice that of the saler and is neutral. After the two spheres are conected by a conducting wire, the charges on the smaller and larger spheres, respectively are:

2) A conducting sphere with radius R is charged until the magnitude of the electric field just outside its surface is E. The electic potential of the sphere, relative to the potential far away is:
(show why please)
a) 0
b) E/R
c)E/R^2
d)ER
e) ER^2

3) A 5cm radius conducting sphere has a charge density of 2*10^-6C/m^2 on its surface. Its electric potetial relative to the potential far away is:

Solution Preview

1)

The potentials on the conductors should be equal when they are conducted by a wire. We also know that the sum of the total charge on these two conductors ...

Solution Summary

With full calculations and explanations, the problems are solved.

A conducting sphere of radius r1 is suspended by a perfectly insulating thread inside and concentric with a larger conducting sphere of radius r2 and the space between the spheres is a vacuum. A charge q is deposited on the outer sphere. What is the potential difference (as would be measured by a voltmeter) between the two spher

Please see the attached file:
3. Consider the case of an infinite conducting cylinder of radius 'a' with a uniform charge per unit length lambda placed in a uniform electric field with the axis of the cylinder perpendicular to the direction of the field. The potential generated by such a system maybe written as: (See attachme

1) Please refer attachment.
2) What are (a) the charge and (b) the chargedensity on the surface of a conducting sphere of radius 0.15m whose potential is 200V ( with V = 0 at infinity)?

The radii of curvature of the spheres of a spherical capacitor is given and to find the charge, chargedensity and work done when it is connected to a battery.
See attached file for full problem description.

Two small plastic spheres each have a mass of 2.00 g and a charge of - 60.0 nC. They are placed 2.80 cm apart.
What is the magnitude of the electric force between the spheres?
By what factor is the electric force on a sphere larger than its weight?

When the distance between the centers of two charged spheres is increased by 10%, how much does the magnitude of the electric force on one of the spheres change?
A. If the two spheres both have the same sign charge, the force decrease about 20$ , but if they have opposite charge it increases by about 20%
B. The force must de

See the attached file.
1. The electrostatic field E in a particular region can be expressed in terms of spherical coordinates. Derive an expression for the potential difference.
2. The electrostatic potential in a region is given by a function. Derive an expression for the electrostatic field in this region, and hence dete

8. A sphere of radius R1 carries a uniform chargedensity p throughout its volume except
for a small spherical hollow volume of radius R2 located at distance a from the center
(and fully contained within the larger sphere).
a) Calculate the electric field E at the center of the hollow sphere. [Be careful, you can't
just ap

Two conducting spheres are concentric, the inner sphere with radius a and the outer sphere with radius b. One sphere is grounded and the other is at potential V0. Find the charge on each when the grounded sphere is (a) the outer one and (b) the inner one.