7.6 Applications of Electrostatics

Why are the metal support rods for satellite network dishes generally grounded?

What are the similarities and differences between the processes in a photocopier and an electrostatic precipitator?

(a) What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? (b) Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces.

The probability of fusion occurring is greatly enhanced when appropriate nuclei are brought close together, but mutual Coulomb repulsion must be overcome. This can be done using the kinetic energy of high-temperature gas ions or by accelerating the nuclei toward one another. (a) Calculate the potential energy of two singly charged nuclei separated by $1.00 \times 10^{−12} \text{m} .$ (b) At what temperature will atoms of a gas h…

(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength of dry air, which is $3.00 \times 10^{6} \text{V}/\text{m}$, if the plates are separated by 2.00 mm and a potential difference of $5.0 \times 10^{3} \text{V}$ is applied? (b) How close together can the plates be with this applied voltage?

A double charged ion is accelerated to an energy of 32.0 keV by the electric field between two parallel conducting plates separated by 2.00 cm. What is the electric field strength between the plates?

A lightning bolt strikes a tree, moving 20.0 C of charge through a potential difference of $1.00 \times 10^{2} \text{MV}.$ (a) What energy was dissipated? (b) What mass of water could be raised from $15 ° \text{C}$ to the boiling point and then boiled by this energy? (c) Discuss the damage that could be caused to the tree by the expansion of the boiling steam.

(a) A sphere has a surface uniformly charged with 1.00 C. At what distance from its center is the potential 5.00 MV? (b) What does your answer imply about the practical aspect of isolating such a large charge?

In one of the classic nuclear physics experiments at the beginning of the twentieth century, an alpha particle was accelerated toward a gold nucleus, and its path was substantially deflected by the Coulomb interaction. If the energy of the doubly charged alpha nucleus was 5.00 MeV, how close to the gold nucleus (79 protons) could it come before being deflected?

A battery-operated car uses a 12.0-V system. Find the charge the batteries must be able to move in order to accelerate the 750 kg car from rest to 25.0 m/s, make it climb a $2.00 \times 10^{2} -\text{m}$ high hill, and finally cause it to travel at a constant 25.0 m/s while climbing with $5.00 \times 10^{2} -\text{N}$ force for an hour.

A uniformly charged half-ring of radius 10 cm is placed on a nonconducting table. It is found that 3.0 cm above the center of the half-ring the potential is –3.0 V with respect to zero potential at infinity. How much charge is in the half-ring?

A CD disk of radius ($R = 3.0 \text{cm}$) is sprayed with a charged paint so that the charge varies continually with radial distance r from the center in the following manner: $\sigma = - \left(6.0 \text{C}/\text{m}\right) r / R$.

Find the potential at a point 4 cm above the center.

A large metal plate is charged uniformly to a density of $\sigma = 2.0 \times 10^{−9} \text{C}/\text{m}^{2}$. How far apart are the equipotential surfaces that represent a potential difference of 25 V?

(a) Find $x > > L$ limit of the potential of a finite uniformly charged rod and show that it coincides with that of a point charge formula. (b) Why would you expect this result?

Two parallel conducting plates, each of cross-sectional area $400 \text{cm}^{2}$, are 2.0 cm apart and uncharged. If $1.0 \times 10^{12}$ electrons are transferred from one plate to the other, (a) what is the potential difference between the plates? (b) What is the potential difference between the positive plate and a point 1.25 cm from it that is between the plates?

Earth has a net charge that produces an electric field of approximately 150 N/C downward at its surface. (a) What is the magnitude and sign of the excess charge, noting the electric field of a conducting sphere is equivalent to a point charge at its center? (b) What acceleration will the field produce on a free electron near Earth’s surface? (c) What mass object with a single extra electron will h…

What can you say about two charges $q_{1} \text{and} q_{2}$, if the electric field one-fourth of the way from $q_{1} \text{to} q_{2}$ is zero?

An electron has an initial velocity of $5.00 \times 10^{6} \text{m}/\text{s}$ in a uniform $2.00 \times 10^{5} -\text{N}/\text{C}$ electric field. The field accelerates the electron in the direction opposite to its initial velocity. (a) What is the direction of the electric field? (b) How far does the electron travel before coming to rest? (c) How long does it take the electron to come to rest? (d) What is the electron’s velocity when it returns to its starting point?

Look up (presumably online, or by dismantling an old device and making measurements) the magnitude of the potential deflection plates (and the space between them) in an ink jet printer. Then look up the speed with which the ink comes out the nozzle. Can you calculate the typical mass of an ink drop?

Calculate the electric field of a dipole throughout space from the potential.