A line of positive charge is formed into a semicircle of radius R = 60.0 cm. The charge per unit length along the semicircle is given by the expression $\lambda=\lambda_{0} \cos \theta.$ The total charge on the semicircle is $12.0 \mu \mathrm{C}$. Calculate the total force on a charge of $3.00 \mu \mathrm{C}$ placed at the center of curvature P.

A sphere of radius 2a is made of a nonconducting material that has a uniform volume charge density $\rho$. (Assume that the material does not affect the electric field.) A spherical cavity of radius $a$ is now removed from the sphere, as shown in the given figure. Show that the electric field within the cavity is uniform and is given by $E_x=0$ and $E_y=$ $\rho a / 3 \epsilon_0$. (Suggestion: The field within the cavity is the superposition of the field due to the original uncut sphere, plus the field due to a sphere the size of the cavity with a uniform negative charge density $-\rho$.

The solubility rules say that $\mathrm{Ba}(\mathrm{OH})_{2}, \mathrm{Sr}(\mathrm{OH})_{2},$ and $\mathrm{Ca}(\mathrm{OH})_{2}$ are marginally soluble hydroxides. Calculate the pH of a saturated solution of each of these marginally soluble hydroxides.

A uniformly charged, straight filament 7.00 m in length has a total positive charge of $2.00 \mu \mathrm{C}$. An uncharged cardboard cylinder 2.00 cm in length and 10.0 cm in radius surrounds the filament at its center, with the filament as the axis of the cylinder. Using reasonable approximations, find (a) the electric field at the surface of the cylinder and (b) the total electric flux through the cylinder.

A solid sphere of radius 40.0 cm has a total positive charge of $26.0 \mu \mathrm{C}$ uniformly distributed throughout its volume. Calculate the magnitude of the electric field $40.0 \mathrm{~cm}$.

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

In nuclear fission, a nucleus of uranium-238, which contains 92 protons, can divide into two smaller spheres, each having 46 protons and a radius of $5.90 \times 10^{-15} \mathrm{m}$. What is the magnitude of the repulsive electric force pushing the two spheres apart?

In nuclear fission, a nucleus of uranium-238, which contains 92 protons, can divide into two smaller spheres, each having 46 protons and a radius of $5.90 \times 10 - 15$ m. What is the magnitude of the repulsive electric force pushing the two spheres apart?

A line of positive charge is formed into a semicircle of radius $R=60.0 \mathrm{~cm}$ as we discussed earlier. The charge per unit length along the semicircle is described by the expression $\lambda=\lambda_0 \cos \theta$. The total charge on the semicircle is $12.0 \mu \mathrm{C}$. Calculate the total force on a we discussed earlier charge of $3.00 \mu \mathrm{C}$ placed at the center of curvature $P$.

A mixture of $\mathrm{N}_{2}, \mathrm{H}_{2},$ and $\mathrm{NH}_{3}$ is at equilibrium [according to the equation $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g).$ The volume is suddenly decreased (by increasing the external pressure) and a new equilibrium is established. If the volume of the final equilibrium mixture is 1.00 L, determine the value of the equilibrium constant, K, for the reaction. Assume temperature is constant.

Four closed surfaces, $S_1$ through $S_4$, together with the charges $-2 Q, Q$, and $-Q$ are sketched in Figure . (The colored lines are the intersections of the surfaces with the page.) Find the electric flux through each surface.

You are a coach for the Physics Olympics team participating in a competition overseas. You are given the following sample problem to present to your team of students, which you need to solve very quickly: A person is standing on the midline of a soccer field. At one end of the field, is a letter D, consisting of a semicircular metallic ring of radius R and a long straight metal rod of length 2R, the diameter of the ring. The plane of the ring is perpendicular to the ground and perpendicular to the midline of the field shown by the broken line. Because of an approaching lightning storm, the semicircular ring and the rod become charged. The ring and the rod each attain a charge Q. What is the electric potential at point P, which is at a position x along the midline of the field, measured from the center of the rod, due to the letter D?

Find the net electric flux through the spherical closed surface as we discussed earlier. The two charges on the right are inside the spherical surface.

Find the net electric flux through (a) the closed spherical surface in a uniform electric field shown in the figure and (b) the closed cylindrical surface shown in the figure. (c) What can you conclude about the charges, if any, inside the cylindrical surface?