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 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.

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?

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?

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) $q_{3}$.

Three-point charges are arranged as we discussed earlier. Find
(a) the magnitude and
(b) the direction of the electric force on the particle at the origin.

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) $q_3$.

A point charge

$$q _ { 1 } = + 5.0 \mu C$$

is fixed in place at x=0, and a point charge

$$q _ { 2 } = - 3.0 \mu \mathrm { C }$$

is fixed at x=-20.0 cm. Where can we place a point charge

$$q _ { 3 } = - 8.0 \mu C$$

so that the net electric force on

$$q_1$$

due to

$$q_2$$

and

$$q_3$$

is zero?

Two small metal spheres are 25.0 cm apart. The spheres have equal amounts of negative charge and repel each other with forces of magnitude 0.036 N. What is the charge on each sphere?

The value of the proportionality constant $k$ in Coulomb's law depends upon the distance between charges.

If the electric forces of repulsion between two 1.0 C charges have magnitude 10 N, how far apart are they?

A metallic sphere has a charge of +4.0 nC. A negatively charged rod has a charge of -6.0 bC. When the rod touches the sphere, $8.2 \times 10^{9}$ electrons are transferred What are the charges of the sphere and the rod now?.

The net force on a charged object surrounded by other charged objects can be calculated through vector addition.

In Coulomb's law, the denominator $r$ represents the radius of the larger charge.