Two very large horizontal sheets are $4.25 \mathrm{~cm}$ apart and carry equal but opposite uniform surface charge densities of magnitude $\sigma$. You want to use these sheets to hold stationary in the region between them an oil droplet of mass $486 \mu \mathrm{g}$ that carries an excess of five electrons. Assuming that the drop is in vacuum.(b) what should $\sigma$ be?

A long line carrying a uniform linear charge density $+50.0 \mu C / m$ runs parallel to and 10.0 cm from the surface of a large, flat plastic sheet that has a uniform surface charge density of $-100 \mu C / m^{2}$ on one side. Find the location of all points where an $\alpha$ particle would feel no force due to this arrangement of charged objects.

Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of $-8.80 \mu \mathrm{C / m^{2}}$, and sheet B, which is to the right of A, carries a uniform charge density of $-11.6 \mu \mathrm{C} / \mathrm{m}^{2}$. Assume that the sheets are large enough to be treated as infinite. Find the magnitude and direction of the net electric field these sheets produce at a point.

(a) 4.00 cm to the right of sheet A;
(b) 4.00 cm to the left of sheet A;
(c) 4.00 cm to the right of sheet B.

Two very large parallel sheets are $5.00 \mathrm{~cm}$ apart. Sheet $A$ carries a uniform surface charge density of $-8.80 \mu \mathrm{C} / \mathrm{m}^2$, and sheet $B$, which is to the right of $A$, carries a uniform charge density of $-11.6 \mu \mathrm{C} / \mathrm{m}^2$. Assume that the sheets are large enough to be treated as infinite. Find the magnitude and direction of the net electric field these sheets produce at a point (c) $4.00 \mathrm{~cm}$ to the right of sheet $B$.

Two very large parallel sheets are $5.00 \mathrm{~cm}$ apart. Sheet $A$ carries a uniform surface charge density of $-8.80 \mu \mathrm{C} / \mathrm{m}^2$, and sheet $B$, which is to the right of $A$, carries a uniform charge density of $-11.6 \mu \mathrm{C} / \mathrm{m}^2$. Assume that the sheets are large enough to be treated as infinite. Find the magnitude and direction of the net electric field these sheets produce at a point (b) $4.00 \mathrm{~cm}$ to the left of sheet $A$;

A very long uniform line of charge has charge per unit length $4.80 \mu \mathrm{C} / \mathrm{m}$ and lies along the $x$-axis. A second long uniform line of charge has charge per unit length $-2.40 \mu \mathrm{C} / \mathrm{m}$ and is parallel to the $x$-axis at $y=0.400 \mathrm{~m}$. What is the net electric field (magnitude and direction) at the following points on the $y$-axis: (b) $y=0.600 \mathrm{~m}$ ?

A very long uniform line of charge has charge per unit length $4.80 \mu \text{C} / \text{m}$ and lies along the x-axis. A second long uniform line of charge has charge per unit length $- 2.40 \mu \text{C} / \text{m}$ is parallel to the x-axis at y = 0.400 m. What is the net electric field (magnitude and direction) at the following points on the y-axis: (a) y = 0.200 m and (b) y = 0.600 m?

What length of mirror drive in an FTIR spectrometer would be required to provide a resolution of

(a) $0.010 \mathrm{~cm}^{-1}$,
(b) $0.50 \mathrm{~cm}^{-1}$
(c) $2.0 \mathrm{~cm}^{-1}$ ?

Suppose that the charge shown in Fig. we saw earlier is fixed in position. A small, positively charged particle is then placed at some location and released. Will the trajectory of the particle follow an electric field line? Why or why not? Suppose instead that the particle is placed at some point in Fig. we saw earlier and released (the positive and negative charges shown are fixed in position). Will its trajectory follow an electric field line? Again, why or why not? Explain any differences between your answers for the two situations.

Two small aluminum spheres, each having mass $0.0250 \textrm{ kg}$, are separated by $80.0 \textrm{ cm}$. How many electrons does each sphere contain? (The atomic mass of aluminum is $26.982 \textrm{ g/mol}$, and its atomic number is $13$.)

Two small aluminum spheres, each having mass $0.0250 \textrm{ kg}$, are separated by $80.0 \textrm{ cm}$. How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude $1.00 \times 10 ^ { 4 } \textrm{ N}$ (roughly $1 \textrm{ ton}$)? Assume that the spheres may be treated as point charges.

Two particles having charges of $+0.500 \mathrm{nC}$ and $+8.00 \mathrm{nC}$ are separated by a distance of $1.20 \mathrm{~m}$.
(a) At what point along the line connecting the two charges is the net electric field due to the two charges equal to zero?
(b) Where would the net electric field be zero if one of the charges were negative?

Two particles having charges $q_1=0.500 \mathrm{~nC}$ and $q_2=8.00 \mathrm{~nC}$ are separated by a distance of $1.20 \mathrm{~m}$. At what point along the line connecting the two charges is the total electric field due to the two charges equal to zero?

A point charge $q _ { 1 } = - 4.00 n C$ is at the point x = 0.600 m, y = 0.800 m, and a second point charge $q _ { 2 } = + 6.00 nC$ is at the point x = 0.600 m, y = 0. Calculate the magnitude and direction of the net electric field at the origin due to these two point charges.