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Which quantity is solenoidal in the electromagnetic theory?
d Explanation: The divergence of the magnetic flux density is zero. This is the Maxwell fourth equation. As the divergence is zero, the quantity will be solenoidal or divergent less.
d
See lessExplanation: The divergence of the magnetic flux density is zero. This is the Maxwell
fourth equation. As the divergence is zero, the quantity will be solenoidal or divergent
less.
The Gauss law employs which theorem for the calculation of charge density?
c 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.
c
See lessExplanation: 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.
The sequence for finding E when charge density is given is
a 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.
a
See lessExplanation: 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.
The charge density of a system with the position vector as electric flux density is
d 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.
d
See lessExplanation: 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.
From the Gauss law for electric field, we can compute which of the following parameters?
c 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.
c
See lessExplanation: 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.
Find the electric flux density of a material whose charge density is given by 12 units in a volume region of 0.5 units.
c 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.
c
See lessExplanation: 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.
In a dipole, the Gauss theorem value will be
b 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.
b
See lessExplanation: 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.
For a solenoidal field, the surface integral of D will be,
a 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.
a
See lessExplanation: 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.
In a medium other than air, the electric flux density will be
d 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.
d
See lessExplanation: 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.
In the medium of free space, the divergence of the electric flux density will be
b 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.
b
See lessExplanation: 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.