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
$64 \times {10^{ - 4}}\,Nm$ and $64 \times {10^{ - 4}}\,J$
$32 \times {10^{ - 4}}\,Nm$ and $32 \times {10^{ - 4}}\,J$
$64 \times {10^{ - 4}}\,Nm$ and $32 \times {10^{ - 4}}\,J$
$32 \times {10^{ - 4}}\,Nm$ and $64 \times {10^{ - 4}}\,J$
A parallel plate capacitor is charged to a potential difference of $100\ V$ and disconnected from the source of emf. A slab of dielectric is then inserted between the plates. Which of the following three quantities change?
$(i)$ The potential difference
$(ii)$ The capacitance
$(iii)$ The charge on the plates
Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x-$ axis at which the net electric field due to these two point charges is zero is
A charge $Q$ is divided into two parts of $q$ and $Q - q$. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of $\frac{Q}{q}$ should be
In the given figure, three capacitors $C_1, C_2$ and $C_3$ are joined to a battery, with symbols having their usual meanings, the correct conditions will be
Four metallic plates, each with a surface area of one side $A$, are placed at a distance $d$ from each other. The plates are connected as shown in the figure. The capacitance of the system between $a$ and $b$ is