This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Vector Properties”.
1. The del operator is called as
d) Vector differential operator
Explanation: The Del operator is used to replace the differential terms, thus called vector differential operator in electromagnetics.
2. The relation between vector potential and field strength is given by
d) Del operator
Explanation: The vector potential and field is given by, E = -Del (V).
3. The Laplacian operator is actually
a) Grad(Div V)
b) Div(Grad V)
c) Curl(Div V)
d) Div(Curl V)
Explanation: The Laplacian operator is the divergence of gradient of a vector, which is also called del2V operator.
4. The divergence of curl of a vector is zero. State True or False.
Explanation: The curl of a vector is the circular flow of flux. The divergence of circular flow is considered to be zero.
5. The curl of gradient of a vector is non-zero. State True or False.
Explanation: The differential flow of flux in a vector is a vector. The curl of this quantity will be zero.
6. Identify the correct vector identity.
a) i . i = j . j = k . k = 0
b) i X j = j X k = k X i = 1
c) Div (u X v) = v . Curl(u) – u . Curl(v)
d) i . j = j . k = k . i = 1
Explanation: By standard proof, Div (u X v) = v . Curl(u) – u . Curl (v).
7. A vector is said to be solenoidal when its
a) Divergence is zero
b) Divergence is unity
c) Curl is zero
d) Curl is unity
Explanation: When the divergence of a vector is zero, it is said to be solenoidal /divergent-free.
8. The magnetic field intensity is said to be
b) Curl free
Explanation: By Maxwell’s equation, the magnetic field intensity is solenoidal due to the absence of magnetic monopoles.
9. A field has zero divergence and it has curls. The field is said to be
a) Divergent, rotational
b) Solenoidal, rotational
c) Solenoidal, irrotational
d) Divergent, irrotational
Explanation: Since the path is not divergent, it is solenoidal and the path has curl, thus rotational.
10. When a vector is irrotational, which condition holds good?
a) Stoke’s theorem gives non-zero value
b) Stoke’s theorem gives zero value
c) Divergence theorem is invalid
d) Divergence theorem is valid
Explanation: Stoke’ theorem is given by, ∫ A.dl = ∫ (Curl A). ds, when curl is zero(irrotational), the theorem gives zero value.
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