Consider a thin spherical shell of radius $R$ with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance r from the centre, is best represented by which graph?

Electric field at a point $(x, y, z)$ is represented by $\vec E = 2x\hat i + {y^2}\hat j$ if potential at $(0,0,0)$ is $2\, volt$ find potential at $(1, 1, 1)$

A spherical conductor of radius $2m$ is charged to a potential of $120\, V$. It is now placed inside another hollow spherical conductor of radius $6m$. Calculate the potential to which the bigger sphere would be raised......$V$

A charge is spread non-uniformly on the surface of a hollow sphere of radius $R$, such that the charge density is given by $\sigma=\sigma_0(1-\sin \theta)$, where $\theta$ is the usual polar angle. The potential at the centre of the sphere is

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

Electric charges of $+10\,\mu\, C, +5\,\mu\, C, -3\,\mu\, C$ and $+8\,\mu\, C$ are placed at the corners of a square of side$\sqrt 2\,m$ . The potential at the centre of the square is