PYQs Based test 4: Electromagnetic Fields

Let aᵣ, a${}_{\text{ϕ},}$ and a${}_z$ be unit vectors along r, ϕ and z directions, respectively in the cylindrical coordinate system. For the electric flux density given by D = (aᵣ 15 + a${}_{\text{ϕ}}$ 2r - a${}_z$ 3rz) Coulomb/m², the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is:

The magnitude of magnetic flux density (B) in micro Teslas (μT), at the centre of a loop of wire wound as a regular hexagon of side length 1 m carrying a current (I = 1 A ) and placed in vacuum as shown in the figure is __________. (Give the answer up to two decimal places.)

The magnetic circuit shown below has uniform cross-sectional area and air gap of 0.2 cm. The mean path length of the core is 40 cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the magnetic flux density computed in the air gap is 1 tesla. With same Ampere-turns, if the core relative permeability is assumed to be 1000 (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is ___________.

Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the zero equipotential curve in the x-yplane is

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is $\frac{Q^2}{4\pi {\epsilon }_0}\frac{K}{d^2}$, where K is given by