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

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

Consider an electric field $$\overrightarrow E = {E_0}\widehat x$$ where $${E_0}$$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is

Which of the field patterns given below is valid for electric field as well as for magnetic field ?