Two point charges are placed on the x-axis as follows: Charge $q _ { 1 } = + 4.00 n C$ is located at x = 0.200 m, and charge $q _ { 2 } = + 5.00 n C$ is at x = -0.300m. What are the magnitude and direction of the total force exerted by these two charges on a negative point charge $\mathrm { q } _ { 3 } = 6.00 nC$ that is placed at the origin?

A point charge $q _ { 1 } = 4.00 \textrm{ nC}$ is placed at the origin, and a second point charge $q _ { 2 } = - 3.00 \textrm{ nC}$ is placed on the x-axis at $x = +20.0 \textrm{ cm}$. A third point charge $q _ { 3 } = 2.00 \textrm{ nC}$ is to be placed on the x-axis between $q _ { 1 }$ and $q _ { 2 }$. (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 $q _ { 3 }$ is placed at $x = +10.0 \textrm{ cm}$?

(b) Where should $q _ { 3 }$ be placed to make the potential energy of the system equal to zero?

A charge of -3.00 nC is placed at the origin of an xy-coordinate system, and a charge of 2.00 nC is placed on the y-axis at y = 4.00 cm. If a third charge, of 5.00 nC, is now placed at the point x = 3.00 cm, y = 4.00 cm, find the x- and y-components of the total force exerted on this charge by the other two charges.

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?

Two point charges are fixed on the y axis: a negative point charge $q_{1}=-25 \mu\mathrm{C}$ at $y_{1}=+0.22 \mathrm{m}$ and a positive point charge $q_{2}$ at $y_{2}=+0.34 \mathrm{m}$. A third point charge $q=+8.4 \mu\mathrm{C}$ is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 27 N and points in the +y direction. Determine the magnitude of $q_{2}$.

Two point charges are placed on the $x$ axis as follows: Charge $q_1=+4.00 \mathrm{nC}$ is located at $x=0.200 \mathrm{~m}$, and charge $q_2=-5.00 \mathrm{nC}$ is at $x=+0.400 \mathrm{~m}$. What are the magnitude and direction of the net force exerted by these two charges on a third point charge $q_3=-0.600 \mathrm{nC}$ placed at the origin?

Two charges are placed on the x axis. One of the charges $\left(q_{1}=+8.5 \mu \mathrm{C}\right)$ is at $x_{1}=+3.0 \mathrm{cm}$ and the other $\left(q_{2}=-21 \mu C\right)$ is at $x_{1}=+9.0 \mathrm{cm}$. Find the net electric field (magnitude and direction) at (a) x=0 cm and (b) x=+6.0 cm.

Point charges $q _ { 1 } = - 4.5 \mathrm { nC }$ and $q _ { 2 } = + 4.5 \mathrm { nC }$ are separated by 3.1 mm, forming an electric dipole. (a) Find the electric dipole moment (magnitude and direction). (b) The charges are in a uniform electric field whose direction makes an angle of $36.9 ^ { \circ }$ with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude $7.2 \times 10 ^ { - 9 } \mathrm { N } \cdot \mathrm { m }$?

A point charge +8.00 nC is on the -x-axis at x=-0.200 m, and a point charge -4.00 nC is on the +x-axis at x=0.200 m. In addition to $x=\pm \infty$, at what point on the x-axis is the resultant field of the two charges equal to zero?

Two positive point charges q are placed on the x-axis, one at $x = a$ and one at $x = -a$.

Find the magnitude and direction of the electric field at $x = 0$.

Two point charges are placed on the $x$ axis. The charge $+2 q$ is at $x=1.5 \mathrm{~m}$, and the charge $-q$ is at $x=-1.5 \mathrm{~m}$. There is a point on the $x$ axis between the two charges where the electric potential is zero. Where is this point?

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.

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?

Two charges, one of 2.50 μC and the other of -3.50 μC, are placed on the x-axis, one at the origin and the other at x = 0.600 m. Find the position on the x-axis where the net force on a small charge +q would be zero.