When a positively charged sphere is brought near a metallic sphere, it is observed that a force of attraction exists between the two. It means

Identical isolated conducting spheres $1$ and $2$ have equal charges and are separated by a distance that is large compared with their diameters (figure $a$). The electrostatic force acting on sphere $2$ due to sphere $1$ is $F$. Suppose that a third identical sphere, having an insulating handle and initially neutral, is touched first to sphere $1$ (figure $b$), then to sphere $2$ (figure $c$), and finally removed (figure $d$). The electrostatic force that now acts on sphere $2$ has magnitude $F^{\text{'}}$. What is the ratio $\frac{F^{\text{'}}}{F}$?

In Figure $\left(a\right)$, particle $1$ (of charge $q_1$) and particle $2$ (of charge $q_2$) are fixed in place on $x$-axis, $8.00 \mathrm{cm}$ apart. Particle $3$ (of charge $q_3=+8.00\times {10}^{-19} \mathrm{C}$) is to be placed on the line between particles $1$ and $2$. Figure $\left(b\right)$ gives the $x$-component of that force versus the $x$-coordinate at which particle $3$ is placed. The scale of the $x$-axis is set by $x_s=8.0 \mathrm{cm}$. What is the sign of charge $q_1$?

In figure $\left(a\right)$, particle $1$ (of charge $q_1$) and particle $2$ (of charge $q_2$) are fixed in place on an $x$-axis, $8.00 \mathrm{cm}$ apart. Particle $3$ (of charge $q_3=+8.00\times {10}^{-19} \mathrm{C}$) is to be placed on the line between particles $1$ and $2$ so that they produce a net electrostatic force $F_{\text{net}}=2F_0$ on it. Figure $\left(b\right)$ gives the $x$-component of that force versus the $x$-coordinate at which particle $3$ is placed. The scale of the x-axis is set by $x_s=8.0 \mathrm{cm}$. What is the ratio $\frac{q_2}{q_1}$?

Figure $\left(a\right)$ shows an arrangement of three charged particles separated by distance $d$. Particles $A$ and $C$ are fixed on the $x$-axis, but particle $B$ can be moved along a circle centred on particle $A$. During the movement, a radial line between $A$ and $B$ makes an angle $\text{θ}$ relative to the positive direction of the $x$-axis (figure $\left(b\right)$) . The curves in figure $\left(c\right)$ give, for two situations, the magnitude $F_{\mathit{\text{net}}}$ of the net electrostatic force on particle $A$ due to the other particles. That net force is given as a function of angle $\text{θ}$ and as a multiple of a basic amount $F_0.$ For example, on curve$1$, at $\text{θ}=180°$ we see that $F_{net}=2F_0$.  For the situation corresponding to curve $1$, what is the ratio of the charge of particle $C$ to that of particle $B$ (including sign)?

Figure $\left(a\right)$ shows an arrangement of three charged particles separated by distance $d$. Particles $A$ and $C$ are fixed on the x-axis, but particle $B$ can be moved along a circle centred on particle $A$. During the movement, a radial line between $A$ and $B$ makes an angle $\text{θ}$ relative to the positive direction of the $x$ -axis (figure $\left(b\right)$). The curves in figure $\left(c\right)$ give, for two situations, the magnitude $F_{\text{net }}$ of the net electrostatic force on particle $A$ due to the other particles. That net force is given as a function of angle $\text{θ}$ and as a multiple of a basic amount $F_0$. For example, on curve$1$, at $\text{θ}=180°$, we see that $F_{\mathrm{net}}=2F_0$.  For the situation corresponding to curve $2$ (dash line) what is the ratio of the charge of particle $C$ to that of particle $B$?

Two small balls having equal positive charge $Q$ (coulomb) on each is suspended by two insulated string of equal length $L$ meter, from a hook fixed to a stand. The whole set-up is taken in a satellite into space where there is no gravity (state of weightlessness). Then the angle between the string and tension in the string is