# Electromagnetic Theory Questions and Answers – Line Integral

«
»

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

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.

2. The integral form of potential and field relation is given by line integral. State True/False
a) True
b) False

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

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.

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

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

Explanation: V = -∫ E.dl = -∫ (-6y/x2 )dx + ( 6/x)dy + 5 dz, from b to a.
On integrating, we get -8.214 volts.

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

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

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.

8. The potential in a lamellar field is
a) 1
b) 0
c) -1
d) ∞

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

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.

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

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. 