Electromagnetic Theory Questions and Answers – Line Integral

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This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Line Integral”.

1. An electric field is given as E = 6y2z i + 12xyz j + 6xy2 k. An incremental path is given by dl = -3 i + 5 j – 2 k mm. The work done in moving a 2mC charge along the path if the location of the path is at p(0,2,5) is (in Joule)
a) 0.64
b) 0.72
c) 0.78
d) 0.80
View Answer

Answer: b
Explanation: W = -Q E.dl
W = -2 X 10-3 X (6y2z i + 12xyz j + 6xy2 k) . (-3 i + 5 j -2 k)
At p(0,2,5), W = -2(-18.22.5) X 10-3 = 0.72 J.
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2. The integral form of potential and field relation is given by line integral. State True/False
a) True
b) False
View Answer

Answer: a
Explanation: Vab = -∫ E.dl is the relation between potential and field. It is clear that it is given by line integral.

3. If V = 2x2y – 5z, find its electric field at point (-4,3,6)
a) 47.905
b) 57.905
c) 67.905
d) 77.905
View Answer

Answer: b
Explanation: E = -Grad (V) = -4xy i – 2×2 j + 5k
At (-4,3,6), E = 48 i – 32 j + 5 k, |E| = √3353 = 57.905 units.
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4. Find the potential between two points p(1,-1,0) and q(2,1,3) with E = 40xy i + 20x2 j + 2 k
a) 104
b) 105
c) 106
d) 107
View Answer

Answer: c
Explanation: V = -∫ E.dl = -∫ (40xy dx + 20x2 dy + 2 dz) , from q to p.
On integrating, we get 106 volts.

5. Find the potential between a(-7,2,1) and b(4,1,2). Given E = (-6y/x2 )i + ( 6/x) j + 5 k.
a) -8.014
b) -8.114
c) -8.214
d) -8.314
View Answer

Answer: c
Explanation: V = -∫ E.dl = -∫ (-6y/x2 )dx + ( 6/x)dy + 5 dz, from b to a.
On integrating, we get -8.214 volts.
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6. The potential of a uniformly charged line with density λ is given by,
λ/(2πε) ln(b/a). State True/False.
a) True
b) False
View Answer

Answer: a
Explanation: The electric field intensity is given by, E = λ/(2πεr)
Vab = -∫ E.dr = -∫ λ/(2πεr). On integrating from b to a, we get λ/(2πε) ln(b/a).

7. A field in which a test charge around any closed surface in static path is zero is called
a) Solenoidal
b) Rotational
c) Irrotational
d) Conservative
View Answer

Answer: d
Explanation: Work done in moving a charge in a closed path is zero. It is expressed as, ∫ E.dl = 0. The field having this property is called conservative or lamellar field.
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8. The potential in a lamellar field is
a) 1
b) 0
c) -1
d) ∞
View Answer

Answer: b
Explanation: Work done in a lamellar field is zero. ∫ E.dl = 0,thus ∑V = 0. The potential will be zero.

9. Line integral is used to calculate
a) Force
b) Area
c) Volume
d) Length
View Answer

Answer: d
Explanation: Length is a linear quantity, whereas area is two dimensional and volume is three dimensional. Thus single or line integral can be used to find length in general.
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10. The energy stored in the inductor 100mH with a current of 2A is
a) 0.2
b) 0.4
c) 0.6
d) 0.8
View Answer

Answer: a
Explanation: dw = ei dt = Li di, W = L∫ i.di
Energy E = 0.5LI2 = 0.5 X 0.1 X 22 = 0.2 Joule.

Sanfoundry Global Education & Learning Series – Electromagnetic Theory.
To practice all areas of Electromagnetic Theory, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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