Explore Exams
Login Signup
Sign in Open App
Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Test  >  Electromagnetic Fields Theory (EMFT)  >  Test: Laplacian Operator - Electrical Engineering (EE) MCQ

Laplacian Operator - Free MCQ Practice Test with solutions, GATE EE Electromagnetic


MCQ Practice Test & Solutions: Test: Laplacian Operator (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: Laplacian Operator". 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

Sign up on EduRev for free to attempt this test and track your preparation progress.

Test: Laplacian Operator - Question 1
Save

The point form of Gauss law is given by, Div(V) = ρv
State True/False.

Detailed Solution: Question 1

Answer: a
Explanation: The integral form of Gauss law is ∫∫∫ ρv dv = V. Thus differential or point form will be Div(V) = ρv.

Test: Laplacian Operator - Question 2
Save

If a function is said to be harmonic, then

Detailed Solution: Question 2

Answer: c
Explanation: Though option a & b are also correct, for harmonic fields, the Laplacian of electric potential is zero. Now, Laplacian refers to Div(Grad V), which is zero for harmonic fields.

Clear all your doubts with EduRev
Test: Laplacian Operator - Question 3
Save

The Poisson equation cannot be determined from Laplace equation. State True/False. 

Detailed Solution: Question 3

Answer: b
Explanation: The Poisson equation is a general case for Laplace equation. If volume charge density exists for a field, then (Del)2V= -ρv/ε, which is called Poisson equation.

Test: Laplacian Operator - Question 4
Save

Given the potential V = 25 sin θ, in free space, determine whether V satisfies Laplace’s equation.

Detailed Solution: Question 4

Answer: a
Explanation: (Del)2V = 0
(Del)2V = (Del)2(25 sin θ), which is not equal to zero. Thus the field does not satisfy Laplace equation.

Test: Laplacian Operator - Question 5
Save

If a potential V is 2V at x = 1mm and is zero at x=0 and volume charge density is -106εo, constant throughout the free space region between x = 0 and x = 1mm. Calculate V at x = 0.5mm.

Detailed Solution: Question 5

Answer: d
Explanation: Del2(V) = -ρv/εo= +106
On integrating twice with respect to x, V = 106. (x2/2) + C1x + C2.
Substitute the boundary conditions, x = 0, V = 0 and x = 1mm, V = 2V in V,
C1 = 1500 and C2 = 0. At x = 0.5mm, we get, V = 0.875V.

Test: Laplacian Operator - Question 6
Save

Find the Laplace equation value of the following potential field
V = x2 – y2 + z2

Detailed Solution: Question 6

Answer: b
Explanation: (Del) V = 2x – 2y + 2z
(Del)2 V = 2 – 2 + 2= 2, which is non zero value. Thus it doesn’t satisfy Laplace equation.

Test: Laplacian Operator - Question 7
Save

Find the Laplace equation value of the following potential field
V = ρ cosφ + z

Detailed Solution: Question 7

Answer: a
Explanation: (Del)2 (ρ cosφ + z)= (cos φ/r) – (cos φ/r) + 0
= 0, this satisfies Laplace equation. The value is 0.

Test: Laplacian Operator - Question 8
Save

Find the Laplace equation value of the following potential field V = r cos θ + φ

Detailed Solution: Question 8

Answer: d
Explanation: (Del)2 (r cos θ + φ) = (2 cosθ/r) – (2 cosθ/r) + 0
= 0, this satisfies Laplace equation. This value is 0.

Test: Laplacian Operator - Question 9
Save

The Laplacian operator cannot be used in which one the following?

Detailed Solution: Question 9

Answer: d
Explanation: The first three options are general cases of Laplacian equation. Maxwell equation uses only divergence and curl, which is first order differential equation, whereas Laplacian operator is second order differential equation. Thus Maxwell equation will not employ Laplacian operator.

Test: Laplacian Operator - Question 10
Save

When a potential satisfies Laplace equation, then it is said to be

Detailed Solution: Question 10

Answer: d
Explanation: A field satisfying the Laplace equation is termed as harmonic field.

10 videos|55 docs|56 tests
Join Course
Information about Test: Laplacian Operator Page
In this test you can find the Exam questions for Test: Laplacian Operator solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Laplacian Operator, EduRev gives you an ample number of Online tests for practice
Download as PDF
;

About this Electrical Engineering (EE) Practice Test

This test contains 10 MCQs on Laplacian Operator 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.

Explore more Electrical Engineering (EE) Study Resources

If you found this Laplacian Operator 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:
  • Video Lectures: covering all the topics of Electromagnetic Fields Theory (EMFT)
  • Notes for Revision: offering revision notes, important questions, summaries, flashcards, cheatsheets & more for Electrical Engineering (EE) preparation
  • MCQ Test: variety of questions as per the pattern of Electrical Engineering (EE) exam
Signup to see your scores go up
within 7 days!
Takes less than 10 seconds to signup