# Electromagnetic Theory Questions and Answers – Magnetic Vector Potential

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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

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

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

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.
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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

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 60x2 varies from (0,0,0) to (1,0,0).
a) 120
b) -20
c) -180
d) 60

Explanation: The field intensity H = -Grad(V). To get V, integrate H with respect to the variable. Thus V = -∫H.dl = -∫60x2 dx = -20x3 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

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

Explanation: The Laplacian of the magnetic vector potential is given by Del2(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

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

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)

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

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