Three point charges are arranged on a line. Charge $q _ { 3 } = + 5.00 n C$ and is at the origin. Charge $q _ { 2 } = - 3.00 n C$ and is at x = +4.00 cm. Charge $q_1$ is at x = +2.00 cm. What is $q_1$ (magnitude and sign) if the net force on $q_3$ is zero?

Neurons are components of the nervous system of the body that transmit signals as electric impulses travel along their length. These impulses propagate when the charge suddenly rushes into and then out of a part of the neuron called an axon. Measurements have shown that, during the inflow part of this cycle, approximately $5.6 \times 10 ^ { 11 } \mathrm { Na } ^ { + }$ (sodium ions) per meter, each with charge $+e$, enter the axon. How many coulombs of charge enters a $1.5-\textrm{ cm}$ length of the axon during this process?

A negative charge of $- 0.550 \mu C$ exerts an upward 0.600-N force on an unknown charge that is located 0.300 m directly below the first charge. What are (a) the value of the unknown charge (magnitude and sign); (b) the magnitude and direction of the force that the unknown charge exerts on the $- 0.550 \mu C$ charge?

In an experiment in space, one proton is held fixed and another proton is released from rest a distance of 2.50 mm away. Sketch qualitative (no numbers!) acceleration–time and velocity–time graphs of the released proton’s motion.

Three point charges are arranged on a coordinate plane such that $5.00\mathrm{~nC}$ is at $(0, 0)$, $6.00\mathrm{~nC}$ at $(0.300m, 0)$ and ${-3.00}\mathrm{~nC}$ at $(0, 0.100m)$.
(a) Find the vector electric field that the $6.00-\mathrm{nC}$ and ${-3.00}-\mathrm{nC}$ charges together create at the origin.
(b) Find the vector force on the $5.00-\mathrm{nC}$ charge.

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.

A point charge q1 = 4.10 nC is placed at the origin, and a second point charge q2 = -2.90 nC is placed on the x-axis at x = + 20.0 cm. A third point charge q3 = 2.00 nC is to be placed on the x-axis between q1 and q2. (Take as zero the potential energy of the three charges when they are infinitely far apart.)

(a) What is the potential energy of the system of the three charges if q3 is placed at x = + 11.0 cm?

(b) Where should q3 be placed between q1 and q2 to make the potential energy of the system equal to zero?

Point charges $q _ { 1 } = 50 \mu \mathrm { C } \text { and } q _ { 2 } = - 25 \mu \mathrm { C }$ are placed 1.0 m apart. (a) What is the electric field at a point midway between them? (b) What is the force on a charge $q _ { 3 } = 20 \mu \mathrm { C }$ situated there?

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

Two fixed point charges are on the $x$-axis. A charge of $-3.00 \mathrm{mC}$ is located at $x=+2.00 \mathrm{~m}$ and a charge of $+5.00 \mathrm{mC}$ is located at $x=-4.00 \mathrm{~m}$. c) Find $E(x)$ for an arbitrary point on the $x$-axis.

The given equation involves a power of the variable. Find all real solutions of the equation.

$$2 x ^ { 5 / 3 } + 64 = 0$$

Point charges $q _ { 1 } = 50 \mu \mathrm { C } \text { and } q _ { 2 } = - 25 \mu \mathrm { C }$ are placed 1.0 m apart. What is the force on a third charge $q _ { 3 } = 20 \mu \mathrm { C }$ placed midway between $q _ { 1 } \text { and } q _ { 2 }$?

Coulomb's law allows us to find the force between two point charges.

Three point charges are held fixed in place as shown in the given figure.

Consider the following comment about this situation:

"There will be zero net electric force on the charge in the middle due to the other charges. Using Coulomb's law, the force due to the $+Q$ charge is positive, and the force due to the $-Q$ charge is negative. The forces cancel."

a. Do you agree with this statement? Explain.

b. How does Coulomb's law apply to situations in which there are more than two point charges?

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.