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Test: Gauss Divergence Theorem - Electrical Engineering (EE) MCQ


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10 Questions MCQ Test Electromagnetic Fields Theory (EMFT) - Test: Gauss Divergence Theorem

Test: Gauss Divergence Theorem for Electrical Engineering (EE) 2024 is part of Electromagnetic Fields Theory (EMFT) preparation. The Test: Gauss Divergence Theorem questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Gauss Divergence Theorem MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Gauss Divergence Theorem below.
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Test: Gauss Divergence Theorem - Question 1

Gauss theorem uses which of the following operations?

Detailed Solution for Test: Gauss Divergence Theorem - Question 1

Answer: c
Explanation: The Gauss divergence theorem uses divergence operator to convert surface to volume integral. It is used to calculate the volume of the function enclosing the region given.

Test: Gauss Divergence Theorem - Question 2

Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x2 + y2 + z2= 9.

Detailed Solution for Test: Gauss Divergence Theorem - Question 2

Answer: b
Explanation: We could parameterise surface and find surface integral, but it is wise to use divergence theorem to get faster results. The divergence theorem is given by ∫∫ F.dS = ∫∫∫ Div (F).dV
Div (3x i + 2y j) = 3 + 2 = 5. Now the volume integral will be ∫∫∫ 5.dV, where dV is the volume of the sphere 4πr3/3 and r = 3units.Thus we get 180π.

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Test: Gauss Divergence Theorem - Question 3

The Gauss divergence theorem converts

Detailed Solution for Test: Gauss Divergence Theorem - Question 3

Answer: d
Explanation: The divergence theorem for a function F is given by ∫∫ F.dS = ∫∫∫ Div (F).dV. Thus it converts surface to volume integral

Test: Gauss Divergence Theorem - Question 4

The divergence theorem for a surface consisting of a sphere is computed in which coordinate system?

Detailed Solution for Test: Gauss Divergence Theorem - Question 4

Answer: d
Explanation: Seeing the surface as sphere, we would immediately choose spherical system, but it is wrong. The divergence operation is performed in that coordinate system in which the function belongs to. It is independent of the surface region.

Test: Gauss Divergence Theorem - Question 5

Find the Gauss value for a position vector in Cartesian system from the origin to one unit in three dimensions.

Detailed Solution for Test: Gauss Divergence Theorem - Question 5

Answer: b
Explanation: The position vector in Cartesian system is given by R = x i + y j + z k. Div(R) = 1 + 1 + 1 = 3. By divergence theorem, ∫∫∫3.dV, where V is a cube with x = 0->1, y = 0->1 and z = 0->1. On integrating, we get 3 units.

Test: Gauss Divergence Theorem - Question 6

The divergence theorem value for the function x2 + y2 + z2 at a distance of one unit from the origin is

Detailed Solution for Test: Gauss Divergence Theorem - Question 6

Answer: d
Explanation: Div (F) = 2x + 2y + 2z. The triple integral of the divergence of the function is ∫∫∫(2x + 2y + 2z)dx dy dz, where x = 0->1, y = 0->1 and z = 0->1. On integrating, we get 3 units.

Test: Gauss Divergence Theorem - Question 7

If a function is described by F = (3x + z, y2 − sin x2z, xz + yex5), then the divergence theorem value in the region 0<x<1, 0<y<3 and 0<z<2 will be

Detailed Solution for Test: Gauss Divergence Theorem - Question 7

Answer: c
Explanation: Div (F) = 3 + 2y + x. By divergence theorem, the triple integral of Div F in the region is ∫∫∫ (3 + 2y + x) dx dy dz. On integrating from x = 0->1, y = 0->3 and z = 0->2, we get 39 units.

Test: Gauss Divergence Theorem - Question 8

Find the divergence theorem value for the function given by (ez, sin x, y2

Detailed Solution for Test: Gauss Divergence Theorem - Question 8

Answer: b
Explanation: Since the divergence of the function is zero, the triple integral leads to zero. The Gauss theorem gives zero value.

Test: Gauss Divergence Theorem - Question 9

For a function given by F = 4x i + 7y j +z k, the divergence theorem evaluates to which of the values given, if the surface considered is a cone of radius 1/2π m and height 4π2 m. 

Detailed Solution for Test: Gauss Divergence Theorem - Question 9

Answer: b
Explanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where dV is the volume of the cone πr3h/3, where r = 1/2π m and h = 4π2 m. On substituting the radius and height in the triple integral, we get 2 units.

Test: Gauss Divergence Theorem - Question 10

Divergence theorem computes to zero for a solenoidal function. State True/False.

Detailed Solution for Test: Gauss Divergence Theorem - Question 10

Answer: a
Explanation: The divergence theorem is given by, ∫∫ F.dS = ∫∫∫ Div (F).dV, for a function F. If the function is solenoidal, its divergence will be zero. Thus the theorem computes to zero.

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