This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Maxwell Law 3”.
1. The charge density of a electrostatic field is given by
a) Curl of E
b) Divergence of E
c) Curl of D
d) Divergence of D
Explanation: From the Gauss law for electric field, the volume charge density is the divergence of the electric flux density of the field. Thus Div(D) = ρv.
2. In the medium of free space, the divergence of the electric flux density will be
Explanation: In free space or air, the charge density will be zero. In other words, the conduction is possible in mere air medium. By gauss law, since the charge density is same as the divergence of D, the Div(D) in air/free space will be zero.
3. In a medium other than air, the electric flux density will be
b) Curl free
Explanation: In any medium other than the air, the conduction is possible, due to the charge carriers. Thus charge density is also non-zero. We can write from Gauss law that Div(D) is non-zero. When the divergence is said to be non-zero, the field is not solenoidal or called as divergent field.
4. For a solenoidal field, the surface integral of D will be,
Explanation: For a solenoidal field, the divergence will be zero. By divergence theorem, the surface integral of D and the volume integral of Div(D) is same. So as the Div(D) is zero for a solenoidal field, the surface integral of D is also zero.
5. In a dipole, the Gauss theorem value will be
Explanation: The Gauss theorem for an electric field is given by Div(D)= ρ. In a dipole only static charge exists and the divergence will be zero. Thus the Gauss theorem value for the dipole will be zero.
6. Find the electric flux density of a material whose charge density is given by 12 units in a volume region of 0.5 units.
Explanation: By Gauss law, Div(D) = ρv. To get D, integrate the charge density given. Thus D = ∫ρv dv, where ρv = 12 and ∫dv = 0.5. We get, D = 12 x 0.5 = 6 units.
7. From the Gauss law for electric field, we can compute which of the following parameters?
Explanation: From the Gauss law for electric field, we can find the electric flux density directly. On substituting, D= ε E, the electric field intensity can be calculated.
8. The charge density of a system with the position vector as electric flux density is
Explanation: The divergence of the electric flux density is the charge density. For a position vector xi + yj + zk, the divergence will be 1 + 1 + 1 = 3. Thus by Gauss law, the charge density is also 3.
9. The sequence for finding E when charge density is given is
Explanation: From the given charge density ρv, we can compute the electric flux density by Gauss law. Since, D = εE, the electric field intensity can also be computed. Thus the sequence is E-D-ρv.
10. The Gauss law employs which theorem for the calculation of charge density?
a) Green theorem
b) Stokes theorem
c) Gauss theorem
d) Maxwell equation
Explanation: The Gauss divergence theorem is given by ∫ D.ds = ∫Div(D).dv. From the theorem value, we can compute the charge density. Thus Gauss law employs the Gauss divergence theorem.
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