A Gaussian surface $S$ encloses two charges $q_1=q$ and $q_2=-q$. The field at $P$ is, 

  

where ${\overrightarrow{E}}_1$, ${\overrightarrow{E}}_2$ and $\overrightarrow{E_3}$ are the field contributed by $q_1$, $q_2$ and $q_3$ at $P$ respectively.

A charged ball $B$ hangs from a silk thread $S$, which makes an angle $\theta$ with a large charged conducting sheet $P$, as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to,

The electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius $10 \mathrm{cm}$ surrounding the total charge is $20 \mathrm{V} \mathrm{m}$. The flux over a concentric sphere of radius $20 \mathrm{cm}$ will be

Electric flux through surface $s_1$:

Two conducting plates, each $3 \mathrm{cm}\times 6 \mathrm{cm}$, and three slabs of dielectric, each $1 \mathrm{cm}\times 3 \mathrm{cm}\times 6 \mathrm{cm}$ and having dielectric constants of $1, 2$ , and $3$ , are assembled into a parallel plate capacitor with $\mathrm{d}=3 \mathrm{cm}$. Determine the two values of capacitance obtained by the two possible methods

of assembling the capacitor. Find $\frac{\left({\mathrm{C}}_{\text{higher }}-{\mathrm{C}}_{\text{Lower }}\right)}{{ϵ}_0}$ (in $\mathrm{cm}$ ). (Approximate the answer to the nearest integer)