Test: Laplacian Operator


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10 Questions MCQ Test Electromagnetic Fields Theory (EMFT) | Test: Laplacian Operator

Test: Laplacian Operator for Electrical Engineering (EE) 2023 is part of Electromagnetic Fields Theory (EMFT) preparation. The Test: Laplacian Operator questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Laplacian Operator MCQs are made for Electrical Engineering (EE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Laplacian Operator below.
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Test: Laplacian Operator - Question 1

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

Detailed Solution for Test: Laplacian Operator - 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

If a function is said to be harmonic, then

Detailed Solution for Test: Laplacian Operator - 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.

Test: Laplacian Operator - Question 3

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

Detailed Solution for Test: Laplacian Operator - 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

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

Detailed Solution for Test: Laplacian Operator - 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

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 for Test: Laplacian Operator - 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

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

Detailed Solution for Test: Laplacian Operator - 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

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

Detailed Solution for Test: Laplacian Operator - 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

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

Detailed Solution for Test: Laplacian Operator - 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

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

Detailed Solution for Test: Laplacian Operator - 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

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

Detailed Solution for Test: Laplacian Operator - Question 10

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

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