Figures below show regular hexagons, with charges at the vertices, In which of the following cases the electric field at the centre is not zero.
$I$
$II$
$III$
$IV$
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
Condenser Ahas a capacity of $15\ \mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity $1\ \mu F$ with air between the plates. Both are charged separately by a battery of $100\,V$ . After charging, both are connected in parallel without the battery and the dielectric material being removed. The common potential now is.......$V$
Two charges $q_1$ and $q_2$ are placed $30\,cm$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\,cm$ from $C$ to $D$. The change in the potential energy of the $\frac{{{q_3}}}{{4\pi \,{ \in _0}}}k$ , where $k$ is
The equivalent capacitance of the combinatio shown in Figure is
A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference $4\,V$. When another parallel combination $n_2$ capacitors, each of value $C_2$, is charged by a source of potential difference $V$, it has the same (total) energy store in it, as the first combination has. The value of $C_2$, in terms of $C_1$, is then