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- Charge is distributed throughout a very long cylindrical volume of radius R such that the charge density increases with the distance r from the central axis of the cylinder according to p=ar , where a is a constant. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E=ar230 (rR); E=aR330r (rR).The conductor in the preceding figure has an excess charge of 5.0C . If a 2.0C point charge is placed in the cavity, what is the net charge on the surface of the cavity and on the outer surface of the conductor?Discuss the role that symmetry plays in the application of Gauss's law. Give examples of continuous charge distributions in which Gauss's law is useful and not useful in determining the electric field.
- Discuss the restrictions on the Gaussian surface used to discuss planar symmetry. For example, is its length important? Does the cross-section have to be square? Must the end faces be on opposite sides of the sheet?A total charge Q is distributed uniformly throughout a spherical shell of inner and outer radii r1 and r2 , respectively. Show that the electric field due to the charge is E =Q40r2(r3r13r23r13)r (rr1); (r1rr2); E =Q40r2r (rr1).The infinite slab between the planes defined by z=a/2 and z=a/2 contains a uniform volume charge density p (see below). What is the electric field produced by this charge distribution, both inside and outside the distribution?
- In this problem, we will go through the famous experiment led by Robert A. Millikan. The charge of the electron that he calculated by this experiment is 0.6% off from the currently accepted value, that too due to the imprecise value of viscosity of air known at the time. This experiment demonstrates that the electric charge of the oil droplet is some integer multiple of electron charge - thereby establishing charge quantization as an experimental fact. It's a free-body diagram. Here, we depict an oil droplet that is falling downwards due to gravity in an air medium. The droplet experiences an upward force due to air friction. When the two forces are on the droplet balance, the droplet falls steadily with velocity vd. Find the friction coefficient k. Given the symbolic expression for the mass of the oil droplet m, acceleration due to gravity g, downward terminal velocity of the droplet vd. Give the answer in terms of these variables. a) Write the mathematical expression for the…Figure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << ahas been removed. What is the direction and magnitude of the fieldat the midpoint of the aperture? Solve this exercise using the relationship for a force on a small patch.A spherical water droplet of radius 25 m carries an excess 250 electrons. What vertical electric field is needed to balance the gravitational force on the droplet at the surface of the earth?
- An uncharged spherical conductor S of radius R has two spherical cavities A and B of radii a and b, respectively as shown below. Two point charges +qa and +qb are placed at the center of the two cavities by using non-conducting supports. In addition, a point charge +q0 is placed outside at a distance r from the center of the sphere. (a) Draw approximate charge distributions in the metal although metal sphere has no net charge. (b) Draw electric field lines. Draw enough lines to represent all distinctly different places.What is the electrostatic force on the particle at the lower-right-hand corner of the square shown here? Write the result in terms of the quantities given in the problem (q, a, and k (Coulomb’s constant). Don’t forget to include both the magnitude and the direction of the net force on that charge.The figure here shows a Gaussian cube of face area Aimmersed in a uniform electric field that has the positivedirection of the z axis. In terms of E and A, what is the fluxthrough (a) the front face (which is in the xy plane), (b) therear face, (c) the top face, and (d) the whole cube?