For the configuration shown in the figure below, suppose ...



For the configuration shown in the figure below, suppose that a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose that the electric field at a point 13.5 cm from the center is measured to be 3.30 [pic]103 N/C radially inward while the electric field at a point 50.0 cm from the center is 2.20 [pic]102 N/C radially outward.

From this information, find the following charges. (Include the sign of the charges.)

(a) the charge on the insulating sphere

(b) the net charge on the hollow conducting sphere

(c) the total charge on the inner and outer surfaces of the hollow conducting sphere

inner surface

outer surface

Consider a long, cylindrical charge distribution of radius R with a uniform charge density [pic]. Find the electric field at distance r from the axis, where r < R.

Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconducting walls, the beads move, and at equilibrium they are a distance R apart. Determine the charge on each bead. (Use k_e for ke, g for the acceleration due to gravity, m, and R as necessary.)

q = [pic][pic]R * sqrt( (mg)/(k_e sqrt(3)) )

Three charged particles are located at the corners of an equilateral triangle as shown in the figure below (q = 1.00 µC, L = 0.750 m). Calculate the total electric force on the 7.00 µC charge.

[pic][pic]0.403 N

[pic][pic]314° (counterclockwise from the +x axis)

Show that the maximum magnitude Emax of the electric field along the axis of a uniformly charged ring occurs at x = a / [pic]2 (see the figure below) and has the value shown below.

[pic]

[pic]

Consider a closed triangular box resting within a horizontal electric field of magnitude E = 7.40 [pic]104 N/C, as shown in the figure below.

[pic]

(a) Calculate the electric flux through the vertical rectangular surface of the box.

[pic][pic]-2.22 kN·m2/C

(b) Calculate the electric flux through the slanted surface of the box.

[pic][pic]2.22 kN·m2/C

(c) Calculate the electric flux through the entire surface of the box.

[pic][pic]0 kN·m2/C

Two infinite, nonconducting sheets of charge are parallel to each other, as shown in the figure below. The sheet on the left has a uniform surface charge density [pic], and the one on the right has a uniform charge density -[pic].

Calculate the electric field at the following points. (Hint: See Example 24.8 in the textbook. Use sigma for [pic]and epsilon_0 for [pic]0, the permittivity of free space.)

(a) to the left of the two sheets

E =

[pic][pic][pic]0 [pic][pic][pic]Magnitude is zero.

(b) in between the two sheets

E = [pic][pic][pic]sigma/epsilon_0 [pic][pic][pic]to the right

(c) to the right of the two sheets

E = [pic][pic][pic]0 [pic][pic][pic]Magnitude is zero.

An infinitely long cylindrical insulating shell of inner radius a and outer radius b has a uniform volume charge density [pic]. A line of uniform linear charge density [pic]is placed along the axis of the shell. Determine the electric field intensity everywhere. (Use epsilon_0 for [pic]0, lambda for [pic], rho for [pic], a, b, and r as necessary.)

r < a: E = [pic][pic][pic]lambda/(2 pi r epsilon_0)[pic]

a < r < b: E = [pic][pic][pic](lambda + rho pi (r^2 - a^2))/(2 pi r epsilon_0)[pic]

r > b: E = [pic][pic][pic](lambda + rho pi (b^2 - a^2))/(2 pi r epsilon_0)[pic]

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