PYQs Based test 5: Electromagnetic Fields

The flux density at a point in space is given by B = 4xaₓ + 2kya${}_y$ + 8a${}_z$ Wb/m² . The value of constant k must be equal to

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the centre of the line joining the electron and proton. At t = 0 , the particles are released but are constrained to move along the same straight line. Which of these will collide first?

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by $\varphi =f\left(r,z\right)$, where $f$ is a continuous function of $r$ and $z$. Let $\vec{E}$ be the resulting electric field. Then the magnitude of $\nabla \times \vec{\mathrm{E}}$

A steady current I is flowing in the –x direction through each of two infinitely long wires at $y=\pm \frac{L}{2}$ as shown in the figure. The permeability of the medium is ${\mu }_0$. The $\vec{B}$ – field at (0, L, 0) is

A 1 μC point charge is held at the origin of a cartesian coordinate system. If a second point charge of 10 μC is moved from (0, 10, 0) to (5, 5, 5) and subsequently to (5, 0, 0), then the total work done is _________ mJ.

(Round off to 2 decimal places).

Take $\frac{1}{4\pi {\epsilon }_o}=9\times 10^9$ in SI units. All coordinates are in meters.