PYQs Based Test - 16 : Electromagnetics

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:

A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ______.

The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is __________ (up to 2 decimal places).

A half wavelength dipole is kept in the x-y plane and oriented along 45° from the x-axis. Determine the direction of null in the radiation pattern for 0 ≤ Φ ≤ π. Here the angle θ (0 ≤ θ ≤ π) is measured from the z-axis, and the angle Φ (0 ≤ Φ ≤ 2π) is measured from the x-axis in the x-y plane.

Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field E2 in the gap to the original electric field E1 is ___________.