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Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Test  >  Electromagnetic Fields Theory (EMFT)  >  Test: Volume Integral - Electrical Engineering (EE) MCQ

Volume Integral - Free MCQ Practice Test with solutions, GATE EE Electromagnetic


MCQ Practice Test & Solutions: Test: Volume Integral (10 Questions)

You can prepare effectively for Electrical Engineering (EE) Electromagnetic Fields Theory (EMFT) with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Volume Integral". These 10 questions have been designed by the experts with the latest curriculum of Electrical Engineering (EE) 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Test: Volume Integral - Question 1
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The divergence theorem converts

Detailed Solution: Question 1

Answer: b
Explanation: The divergence theorem is given by, ∫∫ D.ds = ∫∫∫ Div (D) dv. It is clear that it converts surface (double) integral to volume(triple) integral.

Test: Volume Integral - Question 2
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The triple integral is used to compute volume. State True/False 

Detailed Solution: Question 2

Answer: a
Explanation: The triple integral, as the name suggests integrates the function/quantity three times. This gives volume which is the product of three independent quantities.

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Test: Volume Integral - Question 3
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The volume integral is three dimensional. State True/False

Detailed Solution: Question 3

Answer: a
Explanation: Volume integral integrates the independent quantities by three times. Thus it is said to be three dimensional integral or triple integral.

Test: Volume Integral - Question 4
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Find the charged enclosed by a sphere of charge density ρ and radius a. 

Detailed Solution: Question 4

Answer: b
Explanation: The charge enclosed by the sphere is Q = ∫∫∫ ρ dv.
Where, dv = r2 sin θ dr dθ dφ and on integrating with r = 0->a, φ = 0->2π and θ = 0->π, we get Q = ρ(4πa3/3).

Test: Volume Integral - Question 5
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Evaluate Gauss law for D = 5r2/2 i in spherical coordinates with r = 4m and θ = π/2 as volume integral.

Detailed Solution: Question 5

Answer: b
Explanation: ∫∫ D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.
The divergence of D given is, Div(D) = 5r and dv = r2 sin θ dr dθ dφ. On integrating, r = 0->4, φ = 0->2π and θ = 0->π/4, we get Q = 588.9.

Test: Volume Integral - Question 6
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Compute divergence theorem for D = 5r2/4 i in spherical coordinates between r = 1 and r = 2 in volume integral.

Detailed Solution: Question 6

Answer: c
Explanation: D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.
The divergence of D given is, Div(D) = 5r and dv = r2 sin θ dr dθ dφ. On integrating, r = 1->2, φ = 0->2π and θ = 0->π, we get Q = 75 π.

Test: Volume Integral - Question 7
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Compute the Gauss law for D = 10ρ3/4 i, in cylindrical coordinates with ρ = 4m, z = 0 and z = 5, hence find charge using volume integral.

Detailed Solution: Question 7

Answer: d
Explanation: Q = D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.
The divergence of D given is, Div(D) = 10 ρ2 and dv = ρ dρ dφ dz. On integrating, ρ = 0->4, φ = 0->2π and z = 0->5, we get Q = 6400 π.

Test: Volume Integral - Question 8
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Using volume integral, which quantity can be calculated?

Detailed Solution: Question 8

Answer: c
Explanation: The volume integral gives the volume of a vector in a region. Thus volume of a cube can be computed.

Test: Volume Integral - Question 9
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Compute the charge enclosed by a cube of 2m each edge centered at the origin and with the edges parallel to the axes. Given D = 10y3/3 j.

Detailed Solution: Question 9

Answer: c
Explanation: Div(D) = 10y2
∫∫∫Div (D) dv = ∫∫∫ 10y2 dx dy dz. On integrating, x = -1->1, y = -1->1 and z = -1->1, we get Q = 80/3.

Test: Volume Integral - Question 10
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Find the value of divergence theorem for the field D = 2xy i + x2 j for the rectangular parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.

Detailed Solution: Question 10

Answer: b
Explanation: Div (D) = 2y
∫∫∫Div (D) dv = ∫∫∫ 2y dx dy dz. On integrating, x = 0->1, y = 0->2 and z = 0->3, we get Q = 12.

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About this Electrical Engineering (EE) Practice Test

This test contains 10 MCQs on Volume Integral with detailed solutions for each question. It is part of the Electromagnetic Fields Theory (EMFT) course on EduRev, designed to align with the current Electrical Engineering (EE) syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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If you found this Volume Integral MCQ Test helpful, you can further enhance your Electrical Engineering (EE) preparation with in-depth courses on EduRev, for all the subjects and topics available in Electromagnetic Fields Theory (EMFT) course. The course offers:
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