PYQs Based test 4: Electromagnetic Fields

Divergence of the three-dimensional radial vector field $\vec{r}$ is

A hollow metallic sphere of radius r is kept at potential of 1 Volt. The total electric flux coming out of the concentric spherical surface of radius R (> r) is

The figures show diagrammatic representations of vector fields $\vec{X},\vec{Y},and\vec{Z}$ respectively. Which one of the following choices is true?

Consider a function $\bar{f}=\frac{1}{r^2}\hat{r}$, where r is the distance from the origin and $\hat{r}$ is the unit vector in the radial direction. The divergence of the function over a sphere of radius R, which includes the origin, is

Three capacitors C₁, C₂ and C₃ whose values are 10 μF, 5 μF, and 2 μF respectively, have breakdown of 10 V, 5 V and 2 V respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively