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Chapter 23: Q68P (page 684)
The net electric flux through each face of a die (singular of dice) has a magnitude in units of that is exactly equal to the number of spots Non the face (1 through 6). The flux is inward for Nodd and outward for Neven. What is the net charge inside the die?
The net charge inside the die is .
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A non-conducting solid sphere has a uniform volume charge density P. Letbe the vector from the center of the sphere to a general point Pwithin the sphere.
(a) Show that the electric field at Pis given by(Note that the result is independent of the radius of the sphere.)
(b) A spherical cavity is hollowed out of the sphere, as shown in Fig. 23- 60. Using superposition concepts, show that the electric field at all points within the cavity is uniform and equal to where ais the position vector from the center of the sphere to the center of the cavity.
An infinite line of charge produces a field of magnitudeat distance 2.0 m. Find the linear charge density.
Charge is distributed uniformly throughout the volume of an infinitely long solid cylinder of radius R.
(a) Show that, at a distance r < R from the cylinder axis,where is the volume charge density.
(b) Write an expression for E when r > R.
A particle of charge is at the center of a Gaussian cubeon edge. What is the net electric flux through the surface?
Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the tunnel or outside the ball. Let be the magnitude of the electrostatic force on the proton when it is located at the ball鈥檚 surface, at radius R. As a multiple of R, how far from the surface is there a point where the force magnitude is if we move the proton (a) away from the ball and (b) into the tunnel?
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