In the electric field of a point charge $q$, a certain charge is carried from point $A$ to $B$, $C$, $D$ and $E$. Then the work done
AIs least along the path $AB$
BIs least along the path $AD$
CIs zero along all the paths $AB,\;AC,\;AD$ and $AE$
DIs least along $AE$
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CIs zero along all the paths $AB,\;AC,\;AD$ and $AE$
c (c) $ABCDE$ is an equipotential surface, on equipotential surface no work is done in shifting a charge from one place to another.
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A parallel plate capacitor has an electric field of ${10^5}\,V/m$ between the plates. If the charge on the capacitor plate is $1\,\mu \,C$, the force on each capacitor plate is......$N$
A parallel plate capacitor has a dielectric slab of dielectric constant $K$ between its plates that covers $1 / 3$ of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $C$ while that of the portion with dielectric in between is $C _1$. When the capacitor is charged, the plate area covered by the dielectric gets charge $Q_1$ and the rest of the area gets charge $Q_2$. Choose the correct option/options, igonoring edge effects.
$(A)$ $\frac{E_1}{E_2}=1$ $(B)$ $\frac{E_1}{E_2}=\frac{1}{K}$ $(C)$ $\frac{Q_1}{Q_2}=\frac{3}{K}$ $(D)$ $\frac{ C }{ C _1}=\frac{2+ K }{ K }$
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