The identical isolated conducting spheres $\left(1\right)$ and $\left(2\right)$ have equal charges and are separated by a distance that is large compared with their diameters. The electrostatic force acting on sphere $\left(2\right)$ due to sphere $\left(1\right)$ is $\overrightarrow{F}$. Suppose, now that a third identical sphere $\left(3\right)$, having an insulating handle and initially neutral, is touched first to sphere $\left(1\right)$ then to sphere $\left(2\right)$, then to sphere $\left(1\right)$ again (not shown), and then finally removed. The electrostatic force that now acts on sphere $\left(2\right)$ has magnitude $F^{\text{'}}$. What is the ratio $\frac{F^{\text{'}}}{F}$?

Particles $\left(2\right)$ and $\left(4\right)$ of charge $-e$, are fixed in place on $y-$axis, $y_2=-10.0 \mathrm{cm}$ and $y_4=5.00 \mathrm{cm}$. Particles $\left(1\right)$ and $\left(3\right)$ of charge $-e$, can be moved along the $x-$axis. Particle $\left(5\right)$ of charge $+e$, is fixed at the origin. Initially particle $\left(1\right)$ is at $x_1=-10.0 \mathrm{cm}$ and particle $\left(3\right)$ is at $x_3=10.0 \mathrm{cm}$.

$\left(A\right)$ To what value of $x$, must particle $\left(1\right)$ be moved to rotate the direction of the net electric force ${\overrightarrow{F}}_{\text{net }}$ on particle $\left(5\right)$ by $60°$ counter-clockwise?

$\left(B\right)$ With particle $\left(1\right)$ fixed at its new position, to what value of $x$, must you move particle $\left(3\right)$ to rotate ${\overrightarrow{F}}_{\text{net }}$back to its original direction?

In figure $\left(a\right)$,

Three positively charged particles are fixed on an $x-$axis. Particles $\left(B\right)$ and $\left(C\right)$ are so close to each other that they can be considered to be at the same distance from particle $\left(A\right)$. The net force on particle $\left(A\right)$ due to particles $\left(B\right)$ and $\left(C\right)$ is $2.310\times {10}^{-23} \mathrm{N}$ in the negative direction of the $x-$axis.

In figure $\left(b\right)$,

Particle $\left(B\right)$ has been moved to the opposite side of $\left(A\right)$, but is still at the same distance from it. The net force on $\left(A\right)$ is now $2.877\times {10}^{-24} \mathrm{N}$ in the negative direction of the $x-$axis.

What is the ratio $\frac{q_{\mathrm{C}}}{q_{\mathrm{B}}}$?  

In crystals of the salt cesium chloride. cesium ions $\left({\mathrm{Cs}}^{+}\right)$ form the eight corners of a cube and a chlorine ion $\left({\mathrm{Cl}}^{-}\right)$ is at the cube's center. The edge length of the cube is $0.40 \mathrm{nm}$. $\left({\mathrm{Cs}}^{+}\right)$ ions are each deficient by one electron (thus each has a charge $+e$), and the $\left({\mathrm{Cl}}^{-}\right)$ ion has one excess electron (thus has a charge $-e$).

$\left(A\right)$ What is the magnitude of the net electrostatic force exerted on the $\left({\mathrm{Cl}}^{-}\right)$ ion by the eight $\left({\mathrm{Cs}}^{+}\right)$ ions at the corners of the cube?

$\left(B\right)$ If one of the $\left({\mathrm{Cs}}^{+}\right)$ ions is missing, the crystal is said to have a defect. What is the magnitude of the net electrostatic force exerted on the $\left({\mathrm{Cl}}^{-}\right)$ ion by the seven remaining $\left({\mathrm{Cs}}^{+}\right)$ ions? 

Two particles are fixed on $x-$axis. Particle $\left(1\right)$ of charge $50 \mathrm{\mu C}$ is located at $x=-2.0 \mathrm{cm}$, particle $\left(2\right)$ of charge $Q$ is located at $x=3.0 \mathrm{cm}$ and particle $\left(3\right)$ of charge magnitude $20 \mathrm{\mu C}$ is released from rest on the $y-$axis at $y=2.0 \mathrm{cm}$. What is the value of $Q$, if the initial acceleration of particle $\left(3\right)$ is in the positive direction of the 

$\left(A\right)$ $x-$axis

$\left(B\right)$ $y-$axis

Calculate the number of coulombs of positive charge in $500$ ${\mathrm{cm}}^3$ of (neutral) water.

(A hydrogen atom contains one proton and an oxygen atom contains eight protons.)

Electrons and positrons are produced by the nuclear transformations of protons and neutrons, respectively. The process is termed as beta decay.

$\left(A\right)$ If a proton transforms to a neutron, then is an electron or a positron produced?

$\left(B\right)$ If a neutron transforms to a proton, then is an electron or a positron produced?

Particles $\left(1\right)$ and $\left(2\right)$ of charge $q_1=q_2=+4e$ are on $y$-axis at distance $d=17.0 \mathrm{cm}$ from the origin. Particle $\left(3\right)$ of charge $q_3=+8e$ is moved gradually along the $x$-axis from $x=0$ to $x=+5.0 \mathrm{m}$. At what values of $x$, will the magnitude of the electrostatic force on the third particle from the other two particles be 

$\left(A\right)$ minimum?

$\left(B\right)$ maximum?

What is the

$\left(C\right)$ minimum magnitude?

$\left(D\right)$ maximum magnitude? 

In the figure, particle $1$ (of charge $q_1$) and particle $2$ (of charge $q_2$) are fixed in place, on the $x$-axis, $8.00 \mathrm{cm}$ apart. Particle $3$ $($of charge $q_{3 }=+6.00\times {10}^{-19} \mathrm{C}$) is to be placed on the line between particles $1$ and $2$, so that they produce a net electrostatic force ${\overrightarrow{F}}_{3,\mathrm{net}}$ on it. Figure gives the $x$-component of that force versus the coordinate $x$, at which particle $3$ is placed. The scale of the $x$-axis is set by $x_{\mathrm{n}}=8.0 \mathrm{cm}$. What are $\left(\mathrm{a}\right)$ the sign of charge $q_1$ and $\left(\mathrm{b}\right)$ the ratio $\frac{q_2}{q_1}$?