If an insulated non-conducting sphere of radius $R$ has charge density $\rho .$ The electric field at a distance $r$ from the centre of sphere $(r < R)$ will be
$\frac{{\rho R}}{{3\,{\varepsilon _0}}}$
$\frac{{\rho r}}{{{\varepsilon _0}}}$
$\frac{{\rho r}}{{3\,{\varepsilon _0}}}$
$\frac{{3\rho R}}{{{\varepsilon _0}}}$
Two opposite and equal charges $4 \times {10^{ - 8}}\, coulomb$ when placed $2 \times {10^{ - 2}}\,cm$ away, form a dipole. If this dipole is placed in an external electric field $4 \times 10^8\, newton / coulomb$ , the value of maximum torque and the work done in rotating it through $180^o$ will be
The adjoining diagram shows the electric lines of force emerging from a charged body. If the electric fields at $A$ and $B$ are $E_A$ and $E_B$ respectively and the distance between them is $r$, then
Two capacitors $C_1$ and $C_2 = 2\,C_1$ are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and $C_1$ holds charge $Q$. The switch is closed. At steady state, the charge on capacitors will be
Which graph shows variation of electric field of a uniformly charged sphere $w.r.t.$ distance $(r)$ from the centre
The plates of a parallel plate capacitor are charged up to $100\, volt$. A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$. The dielectric constant of the plate is