Figure we saw earlier shows some of the electric field lines due to three point charges arranged along the vertical axis. All three charges have the same magnitude. (b) At what point(s) is the magnitude of the electric field the smallest? Explain your reasoning. Explain how the fields produced by each individual point charge combine to give a small net field at this point or points.

Two very large horizontal sheets are 4.25 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 $486 \mu g$ that carries an excess of five electrons. Assuming that the drop is in vacuum, (a) which way should the electric field between the plates point, and (b) what should $\sigma$ be?

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?

Three point charges are arranged along the x-axis. Charge $q _ { 1 } = + 3.00 \mu C$ is at the origin, and charge $q _ { 2 } = - 5.00 \mu C$ is at x = 0.200 m. Charge $q _ { 3 } = - 8.00 \mu C$. Where is $q_{3}$ located if the net force on $q_{1}$ is 7.00 N in the – x-direction?

The magnitude of the force on charge A due to charges $B$ and $C$ equals the magnitude of the force due to just $B$ plus the magnitude of the force due to just C.

Three charges $(+q,+q$, and $-q$ ) have equal magnitudes and are located at the vertices of an equilateral triangle. Find the magnitude of the total force on one of the positive charges due to the other two charges.

The two point charges, Q1 and Q2, are located at (1,2,0) and (2,0,0) respectively. Find the relation between Q1 and Q2 such that the total force on a test charge at the point P (-1,1,0) will have a) no x-component, b) no y-component.

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.

Three point charges are arranged as shown in Figure (a) Find the vector electric field that the 6.00-nC and $-3.00-\mathrm{nC}$ charges together create at the origin. (b) Find the vector force on the $5.00-\mathrm{nC}$ charge.

Point charges $q _ { 1 } = + 2.00 \mu \textrm{C}$ and $q _ { 2 } = - 2.00 \mu \textrm{C}$ are placed at adjacent corners of a square for which the length of each side is $3.00 \textrm{ cm}$. Point a is at the center of the square, and point b is at the empty corner closest to $q _ { 2 }$. Take the electric potential to be zero at a distance far from both charges.

(a) What is the electric potential at point a due to $q _ { 1 }$ and $q _ { 2 }$?

(b) What is the electric potential at point b?

(c) A point charge $q _ { 3 } = - 5.00 \mu \textrm{C}$ moves from point a to point $b$. How much work is done on $q _ { 3 }$ by the electric forces exerted by $q _ { 1 }$ and $q _ { 2 }$? Is this work positive or negative?

Two charges $Q _ { 1 } ( + 2.00 \mu \mathrm { C } ) \text { and } Q _ { 2 } ( + 2.00 \mu \mathrm { C } )$ are placed symmetrically along the x-axis at $x = \pm 3.00 \mathrm { cm }$. Consider a charge $Q _ { 3 }$ of charge $+ 4.00 \mu \mathrm { C }$ and mass 10.0 mg moving along the y-axis. If $Q _ { 3 }$ starts from rest at y = 2.00 cm, what is its speed when it reaches y = 4.00 cm?

Three point charges lie along a straight line, where $q_{1}=6.00 \mu \mathrm{C},$ $q_{2}=1.50 \mu \mathrm{C},$ and $q_{3}=-2.00 \mu \mathrm{C}$. The separation distances are $d_{1}=3.00 \mathrm{cm}$ and $d_{2}=2.00 \mathrm{cm}$. Calculate the magnitude and direction of the net electric force on (a) $q_{1},$ (b) $q_{2}$, and (c) $q_{3}$.

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 $B$.