This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Magnetic Vector Potential”.

1. The magnetic vector potential is a scalar quantity.

a) True

b) False

View Answer

Explanation: The magnetic vector potential could be learnt as a scalar. But it is actually a vector quantity, which means it has both magnitude and direction.

2. Find the magnetic field intensity when the magnetic vector potential x i + 2y j + 3z k.

a) 6

b) -6

c) 0

d) 1

View Answer

Explanation: The magnetic field intensity is given by H = -Grad(Vm). The gradient of Vm is 1 + 2 + 3 = 6. Thus H = -6 units.

3. The value of ∫ H.dL will be

a) J

b) I

c) B

d) H

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Explanation: By Stoke’s theorem, ∫ H.dL = ∫ Curl(H).dS and from Ampere’s law, Curl(H) = J. Thus ∫ H.dL = ∫ J.dS which is nothing but current I.

4. Given the vector potential is 16 – 12sin y j. Find the field intensity at the origin.

a) 28

b) 16

c) 12

d) 4

View Answer

Explanation: The field intensity is given by H = – Grad(V). The gradient is given by 0 – 12cos y. At the origin, the gradient will be -12 cos 0 = -12. Thus the field intensity will be 12 units.

5. Find the vector potential when the field intensity 60x^{2} varies from (0,0,0) to (1,0,0).

a) 120

b) -20

c) -180

d) 60

View Answer

Explanation: The field intensity H = -Grad(V). To get V, integrate H with respect to the variable. Thus V = -∫H.dl = -∫60x

^{2}dx = -20x

^{3}as x = 0->1 to get -20.

6. Find the flux density B when the potential is given by x i + y j + z k in air.

a) 12π x 10^{-7}

b) -12π x 10^{-7}

c) 6π x 10^{-7}

d) -6π x 10^{-7}

View Answer

Explanation: The field intensity H = -Grad(V). Since the given potential is a position vector, the gradient will be 3 and H = -3. Thus the flux density B = μH = 4π x 10

^{-7}x (-3) = -12π x 10

^{-7}units.

7. The Laplacian of the magnetic vector potential will be

a) –μ J

b) – μ I

c) –μ B

d) –μ H

View Answer

Explanation: The Laplacian of the magnetic vector potential is given by Del

^{2}(A) = -μ J, where μ is the permeability and J is the current density.

8. The magnetic vector potential for a line current will be inversely proportional to

a) dL

b) I

c) J

d) R

View Answer

Explanation: The magnetic vector potential for the line integral will be A = ∫ μIdL/4πR. It is clear that the potential is inversely proportional to the distance or radius R.

9. The current element of the magnetic vector potential for a surface current will be

a) J dS

b) I dL

c) K dS

d) J dV

View Answer

Explanation: The magnetic vector potential for the surface integral is given by A = ∫ μKdS/4πR. It is clear that the current element is K dS.

10. The relation between flux density and vector potential is

a) B = Curl(A)

b) A = Curl(B)

c) B = Div(A)

d) A = Div(B)

View Answer

Explanation: The magnetic flux density B can be expressed as the space derivative of the magnetic vector potential A. Thus B = Curl(A).

**Sanfoundry Global Education & Learning Series – Electromagnetic Theory.**

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