# Electric Force and Electric Field Problems

The specific principles required are indicated in italics at the beginning of each problem.

1. Electric Force: You and a friend are doing the laundry when you unload the dryer and the discussion comes around to static electricity. Your friend wants to get some idea of the amount of charge that causes static cling. You immediately take two empty soda cans, which each have a mass of 120 grams, from the recycling bin. You tie the cans to the two ends of a string (one to each end) and hang the center of the string over a nail sticking out of the wall. Each can now hangs straight down 30 cm from the nail. You take your flannel shirt from the dryer and touch it to the cans, which are touching each other. The cans move apart until they hang stationary at an angle of 10º from the vertical. Assuming that there are equal amounts of charge on each can, you now calculate the amount of charge transferred from your shirt.

2. Electric Force: You are part of a design team assigned the task of making an electronic oscillator that will be the timing mechanism of a micro-machine. You start by trying to understand a simple model which is an electron moving along an axis through the center and perpendicular to the plane of a thin positively charged ring. You need to determine how the oscillation frequency of the electron depends on the size and charge of the ring for displacements of the electron from the center of the ring which are small compared to the size of the ring. A team member suggests that you first determine the acceleration of the electron along the axis as a function of the size and charge of the ring and then use that expression to determine the oscillation frequency of the electron for small oscillations.

3. Electric Force: You are spending the summer working for a chemical company. Your boss has asked you to determine where a chlorine ion of effective charge -e would situate itself near a carbon dioxide ion. The carbon dioxide ion is composed of 2 oxygen ions each with an effective charge -2e and a carbon ion with an effective charge +3e. These ions are arranged in a line with the carbon ion sandwiched midway between the two oxygen ions. The distance between each oxygen ion and the carbon ion is 3.0 x 10-11 m. Assuming that the chlorine ion is on a line that is perpendicular to the axis of the carbon dioxide ion and that the line goes through the carbon ion, what is the equilibrium distance for the chlorine ion relative to the carbon ion on this line? For simplicity, you assume that the carbon dioxide ion does not deform in the presence of the chlorine ion. Looking in your trusty physics textbook, you find the charge of the electron is 1.60 x 10-19 C.

4. Electric Force: You have been asked to review a new apparatus, which is proposed for use at a new semiconductor ion implantation facility. One part of the apparatus is used to slow down He ions which are positive and have a charge twice that of an electron (He++). This part consists of a circular wire that is charged negatively so that it becomes a circle of charge. The ion has a velocity of 200 m/s when it passes through the center of the circle of charge on a trajectory perpendicular to the plane of the circle. The circle has a charge of 8.0 µC and radius of 3.0 cm. The sample with which the ion is to collide will be placed 2.5 mm from the charged circle. To check if this device will work, you decide to calculate the distance from the circle that the ion goes before it stops. To do this calculation, you assume that the circle is very much larger than the distance the ion goes and that the sample is not in place. Will the ion reach the sample? You look up the charge of an electron and mass of the helium in your trusty Physics text to be 1.6 x 10-19 C and 6.7 x 10-27 Kg.

5. Electric Force: You've been hired to design the hardware for an ink jet printer. You know that these printers use a deflecting electrode to cause charged ink drops to form letters on a page. The basic mechanism is that uniform ink drops of about 30 microns radius are charged to varying amounts after being sprayed out towards the page at a speed of about 20 m/s. Along the way to the page, they pass into a region between two deflecting plates that are 1.6 cm long. The deflecting plates are 1.0 mm apart and charged to 1500 volts. You measure the distance from the edge of the plates to the paper and find that it is one-half inch. Assuming an uncharged droplet forms the bottom of the letter, how much charge is needed on the droplet to form the top of a letter 3 mm high (11 pt. type)?

6. Electric Force: While working in a University research laboratory your group is given the job of testing an electrostatic scale, which is used to precisely measure the weight of small objects. The device consists of two very light but strong strings attached to a support so that they hang straight down. An object is attached to the other end of each string. One of the objects has a very accurately known weight while the other object is the unknown. A power supply is slowly turned on to give each object an electric charge. This causes the objects to slowly move away from each other. When the power supply is kept at its operating value, the objects come to rest at the same horizontal level. At that time, each of the strings supporting them makes a different angle with the vertical and that angle is measured. To test your understanding of the device, you first calculate the weight of an unknown sphere from the measured angles and the weight of a known sphere. Your known is a standard sphere with a weight of 2.000 N supported by a string that makes an angle of 10.00º with the vertical. The unknown sphere's string makes an angle of 20.00º with the vertical. As a second step in your process of understanding this device, estimate the net charge on a sphere necessary for the observed deflection if a string were 10 cm long. Make sure to give the assumptions you used for this estimate.

7. Electric Force: You and a friend have been given the task of designing a display for the Physics building that will demonstrate the strength of the electric force. Your friend comes up with an idea that sounds neat theoretically, but you're not sure it is practical. She suggests you use an electric force to hold a marble in place on a sloped plywood ramp. She would get the electric force by attaching a uniformly charged semicircular wire near the bottom of the ramp, laying the wire flat on the ramp with each of its ends pointing straight up the ramp. She claims that if the charges on the marble and ring and the slope of the ramp are chosen properly, the marble would be balanced midway between the ends of the wire. To test this idea, you decide to calculate the necessary amount of charge on the marble for a reasonable ramp angle of 15 degrees and a semicircle of radius 10 cm with a charge of 800 micro-coulombs. The marble would roll in a slot cut lengthwise into the center of the ramp. The mass of the lightest marble you can find is 25 grams.

8. Electric Force, Gauss's Law: You have a great summer job in a research laboratory with a group investigating the possibility of producing power from fusion. The device being designed confines a hot gas of positively charged ions, called plasma, in a very long cylinder with a radius of 2.0 cm. The charge density of the plasma in the cylinder is 6.0 x 10-5 C/m3. Positively charged Tritium ions are to be injected into the plasma perpendicular to the axis of the cylinder in a direction toward the center of the cylinder. Your job is to determine the speed that a Tritium ion should have when it enters the plasma cylinder so that its velocity is zero when it reaches the axis of the cylinder. Tritium is an isotope of Hydrogen with one proton and two neutrons. You look up the charge of a proton and mass of the tritium in your trusty Physics text to be 1.6 x 10-19 C and 5.0 x 10-27 Kg.

9. Electric and Gravitational Force: You and a friend are reading a newspaper article about nuclear fusion energy generation in stars. The article describes the helium nucleus, made up of two protons and two neutrons, as very stable so it doesn't decay. You immediately realize that you don't understand why the helium nucleus is stable. You know that the proton has the same charge as the electron except that the proton charge is positive. Neutrons you know are neutral. Why, you ask your friend, don't the protons simply repel each other causing the helium nucleus to fly apart? Your friend says she knows why the helium nucleus does not just fly apart. The gravitational force keeps it together, she says. Her model is that the two neutrons sit in the center of the nucleus and gravitationally attract the two protons. Since the protons have the same charge, they are always as far apart as possible on opposite sides of the neutrons. What mass would the neutron have if this model of the helium nucleus works? Is that a reasonable mass? Looking in your physics book, you find that the mass of a neutron is about the same as the mass of a proton and that the diameter of a helium nucleus is 3.0 x 10-13 cm.

10. Electric Field: You are helping to design a new electron microscope to investigate the structure of the HIV virus. A new device to position the electron beam consists of a charged circle of conductor. This circle is divided into two half circles separated by a thin insulator so that half of the circle can be charged positively and half can be charged negatively. The electron beam will go through the center of the circle. To complete the design your job is to calculate the electric field in the center of the circle as a function of the amount of positive charge on the half circle, the amount of negative charge on the half circle, and the radius of the circle.

11. Electric Field: You have a summer job with the telephone company working in a group investigating the vulnerability of underground telephone lines to natural disasters. Your task is to write a computer program which will be used determine the possible harm to a telephone wire from the high electric fields caused by lightning. The underground telephone wire is supported in the center of a long, straight steel pipe that protects it. When lightening hits the ground it charges the steel pipe. You are concerned that the resulting electric field might harm the telephone wire. Since you know that the largest field on the wire will be where it leaves the end of the pipe, you calculate the electric field at that point as a function of the length of the pipe, the radius of the pipe, and the charge on the pipe.