Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Questions  >  The potential field at any point in space con... Start Learning for Free
The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given by
  • a)
    48 ∈0
  • b)
    96 ∈0
  • c)
    144 ∈0
  • d)
    192 ∈0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The potential field at any point in space containing a dielectric mate...
Given, V = (5x2y + 3yz2 + 6xz) Volts and
r = 3
Using Poisson’s equation,

Here,

= 10y + 0 + 6y = 16y 
So,  ρv = -∈ (10y+6y)
∴  ρv|at (1,2,3) = -∈0r (10 x 2 + 6 x 2)
= -∈0 x 3 x 32 = - 96∈0  
= 96∈0 (Magnitude only)
View all questions of this test
Most Upvoted Answer
The potential field at any point in space containing a dielectric mate...
The electric field, E can be calculated from the potential field, V using the relation,

E = -∇V

where ∇ is the gradient operator. The components of the gradient in Cartesian coordinates are given by

∂V/∂x = 10xy + 6z

∂V/∂y = 5x2 + 6xz

∂V/∂z = 3y2 + 6x

Therefore, the electric field at point (1,2,3) is

E = -(∂V/∂x)i - (∂V/∂y)j - (∂V/∂z)k

= -16i - 67j + 21k Volts/meter

The electric field is related to the volume charge density, ρv by the relation,

∇.E = ρv/ε

where ε is the permittivity of the medium. For a dielectric medium of relative permittivity εr, the permittivity is given by

ε = ε0εr

where ε0 is the permittivity of free space.

Therefore, the volume charge density at point (1,2,3) is

ρv = (∇.E)ε/εr

= -63ε0 Volts/meter3

For the given dielectric medium of relative permittivity 3, the permittivity is

ε = ε0εr = 3ε0

Therefore, the volume charge density at point (1,2,3) is

ρv = -63ε0/3 = -21ε0 Volts/meter3

The magnitude of the volume charge density is

|ρv| = 21ε0 Volts/meter3 ≈ 48.5 × 10-12 C/m3

Therefore, the correct option is (a) 48.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer?
Question Description
The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer?.
Solutions for The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE). Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The potential field at any point in space containing a dielectric material of relative permittivity 3 is given by V = (5x2y + 3yz2 + 6xz) Volts, where x, y, z are in meters. The magnitude of volume charge density at point (1,2, 3) will be given bya)48 ∈0b)96 ∈0c)144 ∈0d)192 ∈0Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev