7.6 Applications of electrostatics  (Page 3/12)

Your friend gets really excited by the idea of making a lightning rod or maybe just a sparking toy by connecting two spheres as shown in [link] , and making $R_2$ so small that the electric field is greater than the dielectric strength of air, just from the usual 150 V/m electric field near the surface of the Earth. If $R_1$ is 10 cm, how small does $R_2$ need to be, and does this seem practical? ( Hint: recall the calculation for electric field at the surface of a conductor from Gauss’s Law .)

(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?

A small spherical pith ball of radius 0.50 cm is painted with a silver paint and then $\mathrm{-10}\mu \text{C}$ of charge is placed on it. The charged pith ball is put at the center of a gold spherical shell of inner radius 2.0 cm and outer radius 2.2 cm. (a) Find the electric potential of the gold shell with respect to zero potential at infinity. (b) How much charge should you put on the gold shell if you want to make its potential 100 V?

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?

A point charge of $q=5.0\times {10}^{\mathrm{-8}}\text{C}$ is placed at the center of an uncharged spherical conducting shell of inner radius 6.0 cm and outer radius 9.0 cm. Find the electric potential at (a) $r=4.0\text{cm,}$ (b) $r=8.0\text{cm,}$ (c) $r=12.0\text{cm}\text{.}$

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 have its weight supported by this field?

Point charges of $25.0\mu \text{C}\text{and}45.0\mu \text{C}$ are placed 0.500 m apart.

(a) At what point along the line between them is the electric field zero?

(b) What is the electric field halfway between them?

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?

Calculate the angular velocity $\omega$ of an electron orbiting a proton in the hydrogen atom, given the radius of the orbit is $0.530\times {10}^{\mathrm{-10}}\text{m}$ . You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.

An electron has an initial velocity of $5.00\times {10}^6\text{m/s}$ in a uniform $2.00\times {10}^5\text{-N/C}$ 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?

Three ${\text{Na}}^{+}$ and three ${\text{Cl}}^{\text{−}}$ ions are placed alternately and equally spaced around a circle of radius 50 nm. Find the electrostatic energy stored.

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?

Use the electric field of a finite sphere with constant volume charge density to calculate the electric potential, throughout space. Then check your results by calculating the electric field from the potential.

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