If the electric potential at a single point is known, can E (electric field) at that point be determined?
If so, how? If not, why not?
A positive point charge is placed near a very large conducting plane. A professor of physics asserted that the field caused by this configuration is the same as would be obtained by removing the plane and placing a negative point charge of equal magnitude in the mirror-image position behind the initial position of the plane. Is this correct?
Why or why not?
A proton, an alpha particle, an electron, and a neutron are at rest at the corners of a square whose side length is 5.00 . 10-10 m with the electron and neutron at opposite corners. How minimum an amount of work must be done to move the particles far from each other?
The potential V at a distance of 25.0 cm from a very small charged sphere is 48.0 V, with V taken to be zero at an infinite distance from the sphere. A) If the sphere is treated as a point charge, what is its charge?
B) What is the potential at a distance of 75.0 cm from the sphere?
For each of the following arrangement of two point charges, find all the points along the line passing through both charges for with the electric potential V is zero (take V=0 infinitely far from the charges) and for which the electric field E is zero:
a) charges +Q and +2Q separated by distance d;
b) charges -Q and +2Q separated by a distance d.
Are both V and E zero at the same placed?
Explain.
The electric field at the surface of a charged, solid, copper sphere with radius 0.200 m is 3800 N/C, directed toward the center of the sphere. What is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the sphere?
In the Bohr model of the hydrogen atom, a single electron revolves around a single proton in circle of radius r. Assume that proton remains at rest.
a) By equating of electric force to the electron mass times its acceleration, derive an expression for the electron speed.
b) Obtain an expression for the electron’s kinetic energy, and show that its magnitude is just half that of electric potential energy.
c) Obtain an expression for the total energy, and evaluate it using r=5.29 .10-11m. Give your numerical result in joules and in electron volts.
The tube of a Geiger counter (Problem 23.58) has a long, hollow, metal cylinder 2.00 mm in diameter. Along the axis of the tube is a wire 0.127 mm in diameter running its full length. When the tube is operating, a voltage of 850 V is applied between the two conductors. Find the electric field strength at a) the outer surface of the wire; b) the inner surface of the cylinder.
For the expression for E(r) obtained in Example 22.9 (Section 22.4), find the expression for the electric potential V (r) as a function of r both inside and outside the uniformly charged sphere. Assume that V=0 at infinity. B) Graph V and E as functions of r from r=0 to r=3R
An alpha particle with kinetic energy 11.0 MeV makes a head-on collision with a lead nucleus at rest. What is a distance of closest approach of the two particles?
(Assume that the lead nucleus remains stationary and that it may be treated as a point charge. The atomic number of lead is 82. The alpha particle is a helium nucleus, with atomic number 2.
A hollow, thin-walled insulating cylinder of radius R and length L (like the cardboard tube in a roll of toilet paper) has charge Q uniformly distributed over its surface. A) Calculate the electric potential at the center of the tube. Take the origin to be at the center of the tube, and take the potential to be zero at infinity. B) Show that if L << R, the result of part (a) reduces to the potential on the axis of a ring of charge of radius R (Example 23.11 in section 23.30) c. Use the result of part (a) to find the electric field at all points along the axis of the tube