Test: Divergence


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

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

The divergence of a vector is a scalar. State True/False. 

Detailed Solution for Test: Divergence - 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

 The divergence concept can be illustrated using Pascal’s law. State True/False.

Detailed Solution for Test: Divergence - 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.

Test: Divergence - Question 3

Compute the divergence of the vector xi + yj + zk.

Detailed Solution for Test: Divergence - 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

Find the divergence of the vector yi + zj + xk.

Detailed Solution for Test: Divergence - 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

Given D = e-xsin y i – e-xcos y j
Find divergence of D.

Detailed Solution for Test: Divergence - 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

 Find the divergence of the vector F= xe-x i + y j – xz k 

Detailed Solution for Test: Divergence - 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

 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 for Test: Divergence - 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

Find whether the vector is solenoidal, E = yz i + xz j + xy k

Detailed Solution for Test: Divergence - 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

Find the divergence of the field, P = x2yz i + xz k

Detailed Solution for Test: Divergence - 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

Identify the nature of the field, if the divergence is zero and curl is also zero.

Detailed Solution for Test: Divergence - 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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