For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$
$ - {X^2} - \frac{3}{2}{Y^2} + 5$
$\frac{{ - 2}}{3}{X^2} - \frac{3}{2}{Y^2} + 5$
$ - 2{X^2} - \frac{{3{Y^2}}}{2}$
$\frac{{3{Y^2}}}{2} + 5$
Charges are placed on the vertices of a square as shown. Let $E$ be the electric field and $V$ the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then
A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R ( R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is
Charges are placed on the vertices of a square as shown Let $\vec E$ be the electric field and $V$ the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then
Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$, as shown in the figure. Given that $K=\frac{1}{4 \pi \varepsilon_0} \frac{q}{L^2}$, which of the following statement $(s)$ is (are) correct?
$(A)$ the elecric field at $O$ is $6 K$ along $O D$
$(B)$ The potential at $O$ is zero
$(C)$ The potential at all points on the line $PR$ is same
$(D)$ The potential at all points on the line $ST$ is same.
Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown. If $E$ represents electric field and $V$ represents electric potential at $O$, then