Problem 11.
A thin disk with a circular hole at its center has inner radius a nd outer radius . The disk has a uniform positive surgace charge density on its surface. The disk lies in the yz plane, with its center at the origin.
A point particle with mass m and negative charge q is free to move along the x axis (but cannot move off the axis). The particle is originally placed at rest at x=0.01 and released. Find the frequency of oscillations.
Solution
Problem 12.
Suppose that of hydrogen is separated into its constituent protons and electrons, and that the protons are all grouped together at one point, and the electrons at another point, 3 meter distant. What is the magnitude of the force between the two groups of charge?
Solution
Problem 13.
Two small beads having positive charges 25q and q are fixed at the opposite ends of a horizontal insulating rod, extending from the origin (the location of the larger charge) to the point x = d. A third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium?
Solution
Problem 14.
Each of the protons in a particle beam has a kinetic energy of . What are the magnitude and direction of the electric field that will stop these protons in a distance of 2 m?
Solution
Problem 15.
Two identical spheres are each attached to a rope of length 1 m and hung from a common point. Each sphere has mass 1 kg. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. The spheres have positive charges. The spheres are in equilibrium and each rope makes an angle 30 degrees with the vertical. Find the tension of the ropes.
Solution
Problem 16.
A solid metal sphere with radius 0.75 m carries a net charge of 0.13 nC. Find the magnitude of the electric field at the following locations:
a) at a point 0.15 m outside the surface of the sphere.
b) at a point outside the sphere, 0.1 m below the surface.
Solution
Problem 17.
How many excess electrons must be added to an isolated spherical conductor 27 cm in diameter to produce an electric field of 1450 N/C just outside the surface?
Solution
Problem 18.
To study the structure of the lead nucleus, electrons are fixed at a lead target. Some of the electrons actually enter the nuclei of the target, and the deflection of these electrons is measured. The deflection is caused by the charge of the nucleus, which is distributed approximately uniformly over the spherical volume of the nucleus. A lead nucleus has a charge of +82e ( ) and a radius of . Find the acceleration of an electron at the following distances from the center of a nucleus.
(a) R
(b) 2R
(c) R/2
(d) 0 (at the center)
Solution
Problem 19.
An electrostatic field is given by
Determine the work done in moving the charge
(a) from (0,0,0) to (4,0,0) m
(b) from (4,0,0) to (4,2,0) m
(c) from (4,2,0) to (0,0,0) m along a straight path.
Solution
Problem 20.
A cylinder with radius r= 0.75 m and length l=0.6 m that has an infinite line of positive charge running along its axis. The charge per unit length on the line is .
(a) What is the electric flux through the cylinder due to this line of charge?
(b) What is the flux through the cylinder if its radius increased to r= 0.32 m?
(c) What is the flux through the cylinder if its length increased to l= 0.8 m?
Solution
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