An infinitely long thin wire, having a uniform charge density per unit length of $5 nC / m$, is passing through a spherical shell of radius $1 m$, as shown in the figure. A $10 nC$ charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points $P$ and $R$, in Volt, is. . . .

[Given: In SI units $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9, \ln 2=0.7$. Ignore the area pierced by the wire.]

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.

The radius of nucleus of silver (atomic number $=$ $47$) is $3.4 \times {10^{ - 14}}\,m$. The electric potential on the surface of nucleus is $(e = 1.6 \times {10^{ - 19}}\,C)$

Two large vertical and parallel metal plates having a separation of $1 \ cm$ are connected to a $DC$ voltage source of potential difference $X$. A proton is released at rest midway between the two plates. It is found to move at $45^{\circ}$ to the vertical $JUST$ after release. Then $X$ is nearly

The electric potential at the surface of an atomic nucleus $(z=50)$ of radius $9 \times 10^{-13} \mathrm{~cm}$ is ________$\times 10^6 \mathrm{~V}$.

Consider the points lying on a straight line joining two fixed opposite charges. Between the charges there is