PYQs Based test 5: Electromagnetic Fields

Let $\vec{\mathrm{E}}(\mathrm{x},\mathrm{y},\mathrm{z})=2{\mathrm{x}}^2\hat{\mathrm{i}}+5y\hat{\mathrm{j}}+3z\hat{\mathrm{k}}$ The value of ∭${}_V$$(\vec{\nabla }.\vec{E})dV$, where V is the volume enclosed by the unit cube defined by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and 0 ≤ z ≤ 1 is

A conducting square loop of side length 1 m is placed at a distance of 1 m from a long straight wire carrying a current l = 2 A as shown below. The mutual inductance, in nH (rounded off to 2 decimal places), between the conducting loop and the long wire is _____,

The static electric field inside a dielectric medium with relative permittivity εᵣ = 2.25, expressed in cylindrical coordinate system is given by the following expression

$E=a_{r}2r+a_{\varphi }\left(\frac{3}{r}\right)+a_{z}6$

Where aᵣ, a${}_{\text{ϕ}}$, a${}_z$ are unit vectors along r, ϕ and z directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittvity, ε₀, in SI units is given by

A thin soap bubble of radius, R = 1 cm and thickness a = 3.3 μm (a ≪ R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is 4πR²a and that of the drop is $\frac{4}{3}\pi r^3$. The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is ________. (Give the answer up to two decimal places.)

The magnitude of magnetic flux density $\left(\vec{B}\right)$ at a point having normal distance d meters from an infinitely extended wire carrying current of 1 A is $\frac{{\mu }_{0}I}{2nd}$ (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction μ₀ is permeability of free space Assume $\hat{I},\hat{J},\hat{K}$ to be unit vectors along x, y and z axes respectively.



Assuming right handed coordinate system, magnetic field intensity, at coordinate (2, 1, 0) will be