1) A electric dipole is placed at the origin with the two opposite charges located on the x-axis. An electron is fired from far away along the x-axis towards the negative side of the dipole with a speed of 6.0 x 106 m/s and comes to a stop 2 cm from the center of the dipole. (You can assume the distance from the electron to the center of the dipole is much larger than the dipole separation.)
a.Using the concept of forces and fields, explain why the electron comes to a stop. Include a diagram showing the forces involved as part of your explanation.
b. Using the concept of energy, explain why the electron comes to a stop. Include an energy bar chart as part of your explanation. (In ydur bar chart, treat the interaction between the electron and each individual charge of the dipole as a separate interaction.)
c. What is the magnitude of the dipole moment?
2) An insulating rod is bent into the semicircle of radius R shown in the figure. The rod is divided into three sections of equal length.
A charge -q is placed on the middle section of the rod, and a charge +2q is placed on both the top and bottom sections of the rod.
a. Find an expression for the electric field Eat the center of the semicircle. Give your answer in component form.
b. Explain (in words) why your answer to part (a) makes sense based on the arrangement of charge on the semicircle.
c. Evaluate the field strength if R = 10 cm and q = 10 nC.
3) A long 1.0-cm-diameter wire with a linear charge density of 3.0 pC/m runs down the center of two long, thin, concentric cylindrical shells with radii of 4.0 and 7.0 cm. The linear charge density is 5.0 pC/m on the inner shell and -7.0 pC/m on the outer shell.
a. Draw a picture of the charged shells and of an appropriate Gaussian surface that can be used to analyze the electric field. The picture does not have to be three-dimensional; it should simply show the Gaussian surface in relation to the charged shells.
b. Draw a graph of the electric field as a function of the distance from the center of the wire. Your graph must have a reasonable numerical scale for both axes.
4) A parallel-plate capacitor has 3.0 cm x 3.0 cm electrodes with a charge of ±0.025 nC on each plate. A horizontal beam of protons traveling at 1 x 105 m/s enters the center of the capacitor, while a horizontal beam of electrons traveling at 4 x 106 m/s enters the center of the capacitor from the other end.
a. How far apart are the particle beams when they exit the capacitor from the opposite site?
b. How fast are the protons and electrons traveling when they exit the capacitor?