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

Divergence - Free MCQ Practice Test with solutions, GATE EE Electromagnetic


MCQ Practice Test & Solutions: Test: Divergence (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: Divergence". 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: Divergence - Question 1
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The divergence of a vector is a scalar. State True/False. 

Detailed Solution: Question 1

Answer: a
Explanation: Divergence can be computed only for a vector. Since it is the measure of outward flow of flux from a small closed surface as the volume shrinks to zero, the result will be directionless (scalar).

Test: Divergence - Question 2
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 The divergence concept can be illustrated using Pascal’s law. State True/False.

Detailed Solution: Question 2

Answer: a
Explanation: Consider the illustration of Pascal’s law, wherein a ball is pricked with holes all over its body. After water is filled in it and pressure is applied on it, the water flows out the holes uniformly. This is analogous to the flux flowing outside a closed surface as the volume reduces.

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Test: Divergence - Question 3
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Compute the divergence of the vector xi + yj + zk.

Detailed Solution: Question 3

Answer: d
Explanation: The vector given is a position vector. The divergence of any position vector is always 3.

Test: Divergence - Question 4
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Find the divergence of the vector yi + zj + xk.

Detailed Solution: Question 4

Answer: b
Explanation: Div (yi + zj + xk) = Dx(y) + Dy(z) + Dz(x), which is zero. Here D refers to partial differentiation.

Test: Divergence - Question 5
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Given D = e-xsin y i – e-xcos y j
Find divergence of D.

Detailed Solution: Question 5

Answer: d
Explanation: Div (D) = Dx(e-xsin y) + Dy(-e-xcos y ) = -e-xsin y + e-xsin y = 0.

Test: Divergence - Question 6
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 Find the divergence of the vector F= xe-x i + y j – xz k 

Detailed Solution: Question 6

Answer: a
Explanation: Div(F) = Dx(xe-x) + Dy(y)+Dz(-xz) = -xe-x + e-x + 1 – x =
e-x(1 – x) + (1 – x) = (1 – x)(1 + e-x).

Test: Divergence - Question 7
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 Determine the divergence of F = 30 i + 2xy j + 5xz2 k at (1,1,-0.2) and state the nature of the field.

Detailed Solution: Question 7

Answer: b
Explanation: Div(F) = Dx(30) + Dy(2xy) + Dz(5xz2) = 0 + 2x + 10xz = 2x + 10xz
Divergence at (1,1,-0.2) will give zero. As the divergence is zero, field is solenoidal.
Alternate/Shortcut: Without calculation, we can easily choose option b, as by theory when the divergence is zero, the vector is solenoidal. Option b is the only one which is satisfying this condition.

Test: Divergence - Question 8
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Find whether the vector is solenoidal, E = yz i + xz j + xy k

Detailed Solution: Question 8

Answer: a
Explanation: Div(E) = Dx(yz) + Dy(xz) + Dz(xy) = 0. The divergence is zero, thus vector is divergentless or solenoidal.

Test: Divergence - Question 9
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Find the divergence of the field, P = x2yz i + xz k

Detailed Solution: Question 9

Answer: b
Explanation: Div(P) = Dx(x2yz) + Dy(0) + Dz(xz) = 2xyz + x, which is option b. For different values of x,y,z the divergence of the field varies.

Test: Divergence - Question 10
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Identify the nature of the field, if the divergence is zero and curl is also zero.

Detailed Solution: Question 10

Since the vector field does not diverge (moves in a straight path), the divergence is zero. Also, the path does not possess any curls, so the field is irrotational.

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About this Electrical Engineering (EE) Practice Test

This test contains 10 MCQs on Divergence 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 Divergence 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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