Three small spheres $x\text{,} y$ and $z$ carry charges of equal magnitudes and with signs shown in figure. They are placed at the vertices of an isosceles triangle with the distance between $x$ and $z$. The spheres $y$ and $z$ are held in place but sphere $x$ is free to move on a frictionless surface.

(a) What is the direction of the electric force on sphere $x$ at the point shown in the figure?

(b) Which path is sphere $x$ likely to take when released?

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 $\theta$.

Two pieces of plastic, a full ring and a half ring, have the same radius and charge density. Which electric field at the centre has the greater magnitude? Define your answer.

Two semi-circular wires $ABC$ and $ADC$, each of radius $R$, are lying on $x-y$ and $x-z$  planes, respectively, as shown in the figure. If the linear charge density of the semi-circular parts and straight parts is $\mathrm{\lambda }$, find the electric field intensity $\overrightarrow{E}$ at the origin.

An infinite wire having linear charge density $\lambda$ is arranged as shown in the figure. A charge particle of mass $m$ and charge $q$ is released from point $P$. Find the initial acceleration of the particle (at $t=0$) just after the particle is released.