Two identical point charges having magnitude $q$ each are placed as shown in figure. If we place a negative charge (of magnitude $-q$ and mass $m$) at the midpoint of charges and displaced along the $\mathrm{X}$– axis, examine whether it will perform the simple harmonic motion. If yes, then find the time period of oscillation of the particle.

Three points charges of $+2 \mathrm{\mu }\mathrm{C}\text{, }-3 \mathrm{\mu }\mathrm{C}$ and $-3 \mathrm{\mu }\mathrm{C}$ are kept at the vertices $\mathrm{A}\text{,} \mathrm{B}$ and $\mathrm{C}$ respectively of an equilateral triangle of side $20 \mathrm{c}\mathrm{m}$ as shown in the figure. What should be the sign and magnitude of the charge $\left(q\right)$ to be placed at the midpoint $\left(\mathrm{M}\right)$ of side $\mathrm{BC}$ so that the charge at $\mathrm{A}$ remains in equilibrium?

Two small spheres, each of mass $m$, are suspended by light strings of length $l$ as shown in the figure. A uniform electric field is applied in the $\mathrm{X}$– direction. The spheres have charges equal to $-q$ and $+q$. Determine the electric field that enables the spheres to be in equilibrium at an angle of $\theta$.

Is an electric field of the type shown by the electric lines in the figure physically possible?

Figure shows three electric field lines.

At which point, $\mathrm{A}$ or $\mathrm{B}$, will the acceleration of the test charge be greater if the charge is released?

Figure shows that $E$ has the same value for all points in front of an infinitely charged sheet. Is this reasonable? One might think that the field should be stronger near the sheet, because the charges are so much closer