UNIT 1
4 Marks:
1. If 𝐴 = 3𝑎𝑥 + 2𝑎𝑦 − 6𝑎𝑧 𝑎𝑛𝑑 𝑏 = 4𝑎𝑥 + 3𝑎𝑦 , determine𝐴. 𝐵 𝑎𝑛𝑑 |𝐴 × 𝐵|
2. Find the volume of a sphere of radius ‘a’ from the differential volume of spherical capacitor.
3. Determine the vector A directed from (2,-4,1) to (0,-2,0) in Cartesian coordinates and also find the unit vector
of A.
4. Find the divergence of the given vector at (2,-2,9) 𝐴 = 𝑥 2 𝑎𝑥 + (𝑥𝑦)2 𝑎𝑦 + 24𝑥 2 𝑦 2 𝑧 3 𝑎𝑧
10
5. Given the potential V = 𝑟2 sin 𝜃 cos ∅. Find the electric field intensity E at (2,𝜋/2, 0).
6. Prove that ∇ . 𝐷 = 𝜌𝑣 by taking all assumptions.
7. In a cylindrical conductor of radius 2mm, the current density varies with distance from the axis according to
J=103𝑒 −400𝑟 A/m2. Find the total current I
8. An electric field E=3az+4ay-12az mV/m exists in dielectric material which has permittivity of 3. Obtain energy
density.
9. Explain how the relaxation time of conductor is less compared to insulator?
10. Explain how the relaxation time of conductor is less compared to insulator?
11.Prove that: 1 + 𝜒𝑒 = 𝜀𝑟 .
12.Find the capacitance of parallel plate capacitor structure has 500mm side plates of square shape separated by 10mm
distance. A sulphur slab of 6mm thickness with relative permitivity=4 is kept on the lower plate.
13.If 𝑉 = 𝜌2 𝑧 cos(2𝜙), Find E.
14.Explain, under what condition∇ × 𝐸 = 0.
𝜋 𝜋
15.If 𝑃 = 𝜌 sin 𝜙 𝑎𝜌 + 𝜌2 𝑧 𝑎𝜙 + 𝑧 cos 𝜙 𝑎𝑧 , find∇ × 𝑃 𝑎𝑡 (1, 2 , 3 ), Is P is irrotational?
16.If C1= 10µF, C2= 500µF calculate for both series and parallel connection, find the total energy stored in the capacitor
structure with a steady applied potential difference of 100V.
UNIT 1
2 Marks:
1. The curl of a gradient of a scalar field is _____.
2 If the z=15m carries a charge 30C/m2, then the electric field intensity at the origin is ____.
3 The volume charge density associated with the field D= 2xy 2 ax+ yx2 ay+ 2z az at point (1, 1, 0) is
______.
4 A capacitor has a capacitance C=2 micro F. If a voltage of 100V is applied to it, the maximum energy
stored will be_____.
5 What is the charge density for perfect conductors inside the surfaces? Justify.
6 Write down the Poisson’s equation for free space.
7 For copper the conductivity σ= 5.8*10^7 S/m, the relative permittivity = 1. The relaxation time _____.
8 A parallel plate capacitor with a large area is situated in air. When a potential difference 100V between
the plates is applied, the stored energy 44.21 µJ/m2. Find the distance of separation between plates.
9 Verify V= 100x2-10y+z2 is Laplacian or not at origin.
10 A point charge of 30nC is located at the origin while plane y=3 carries charge 10nC/m2. Find D at (0, 4, 3).
11 A vector P⃗ is given by 𝑷⃗ = 𝒙3𝒚𝒂𝒙
̂ − 𝒙2𝒚2𝒂𝒚
̂ − 𝒙2𝒚𝒛𝒂𝒛
̂ which one of the following statements is TRUE?
(A) P⃗ is solenoidal, but not irrotational
(B) P⃗ is irrotational, but not solenoidal
(C) P⃗ is neither solenoidal nor irrotational
(D) P⃗ is both solenoidal and irrotational
12 The direction of vector A is radially outward from the origin, with |A|=krn , where r2 = x2 +y2 +z2 and k is a
constant. The value of n for which ∇⋅A=0is____.
13 Given the vector 𝑨 = (cosx)(siny)𝑎
̂𝑥 + (sinx)(cosy)𝑎̂𝑦 where ̂
𝑎𝑥 , 𝑎̂𝑦 denote unit vectors
along x,y directions, respectively. The magnitude of curl of A is ________
14 In a source free region in vacuum, if the electrostatic potential 𝜑 = 𝟐𝑥 2 + 𝑦 2 + 𝑐𝑧 2 , the value of
constant c must be _______.
15 A vector field 𝐷 = 𝟐𝜌2 𝑎𝜌 ̂ exists inside a cylindrical region enclosed by the surfaces ρ = 1, z = 0 and z=5.
̂ + 𝑧𝑎𝑧
Let S be the surface bounding this cylindrical region. The surface integral of this field on (∯s D⋅ds) is______.
16 The force on a point charge +q kept at a distance d from the surface of an infinite grounded metal plate in a
medium of permittivity ∈ is
(A) 0
(B) q2/16π∈d2 away from the plate
(C) q2/16π∈d2 towards the plate
(D) q2/4π∈d2 towards the plate
