Electromagnetic Theory Questions and Answers – Divergence

«
»

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

1. The divergence of a vector is a scalar. State True/False.
a) True
b) False
View Answer

Answer: a
Explanation: Divergence can be computed only for a vector. Since it is the measure of outward flow of flux from a small closed surface as the volume shrinks to zero, the result will be directionless (scalar).
advertisement

2. The divergence concept can be illustrated using Pascal’s law. State True/False.
a) True
b) False
View Answer

Answer: a
Explanation: Consider the illustration of Pascal’s law, wherein a ball is pricked with holes all over its body. After water is filled in it and pressure is applied on it, the water flows out the holes uniformly. This is analogous to the flux flowing outside a closed surface as the volume reduces.

3. Compute the divergence of the vector xi + yj + zk.
a) 0
b) 1
c) 2
d) 3
View Answer

Answer: d
Explanation: The vector given is a position vector. The divergence of any position vector is always 3.
advertisement
advertisement

4. Find the divergence of the vector yi + zj + xk.
a) -1
b) 0
c) 1
d) 3
View Answer

Answer: b
Explanation: Div (yi + zj + xk) = Dx(y) + Dy(z) + Dz(x), which is zero. Here D refers to partial differentiation.

5. Given D = e-xsin y i – e-xcos y j
Find divergence of D.
a) 3
b) 2
c) 1
d) 0
View Answer

Answer: d
Explanation: Div (D) = Dx(e-xsin y) + Dy(-e-xcos y ) = -e-xsin y + e-xsin y = 0.
advertisement

6. Find the divergence of the vector F= xe-x i + y j – xz k
a) (1 – x)(1 + e-x)
b) (x – 1)(1 + e-x)
c) (1 – x)(1 – e)
d) (x – 1)(1 – e)
View Answer

Answer: a
Explanation: Div(F) = Dx(xe-x) + Dy(y)+Dz(-xz) = -xe-x + e-x + 1 – x =
e-x(1 – x) + (1 – x) = (1 – x)(1 + e-x).

7. Determine the divergence of F = 30 i + 2xy j + 5xz2 k at (1,1,-0.2) and state the nature of the field.
a) 1, solenoidal
b) 0, solenoidal
c) 1, divergent
d) 0, divergent
View Answer

Answer: b
Explanation: Div(F) = Dx(30) + Dy(2xy) + Dz(5xz2) = 0 + 2x + 10xz = 2x + 10xz
Divergence at (1,1,-0.2) will give zero. As the divergence is zero, field is solenoidal.
Alternate/Shortcut: Without calculation, we can easily choose option “0, solenoidal”, as by theory when the divergence is zero, the vector is solenoidal. “0, solenoidal” is the only one which is satisfying this condition.
advertisement

8. Find whether the vector is solenoidal, E = yz i + xz j + xy k
a) Yes, solenoidal
b) No, non-solenoidal
c) Solenoidal with negative divergence
d) Variable divergence
View Answer

Answer: a
Explanation: Div(E) = Dx(yz) + Dy(xz) + Dz(xy) = 0. The divergence is zero, thus vector is divergentless or solenoidal.

9. Find the divergence of the field, P = x2yz i + xz k
a) xyz + 2x
b) 2xyz + x
c) xyz + 2z
d) 2xyz + z
View Answer

Answer: b
Explanation: Div(P) = Dx(x2yz) + Dy(0) + Dz(xz) = 2xyz + x, which is 2xyz + x. For different values of x, y, z the divergence of the field varies.
advertisement

10. Identify the nature of the field, if the divergence is zero and curl is also zero.
a) Solenoidal, irrotational
b) Divergent, rotational
c) Solenoidal, irrotational
d) Divergent, rotational
View Answer

Answer: c
Explanation: Since the vector field does not diverge (moves in a straight path), the divergence is zero. Also, the path does not possess any curls, so the field is irrotational.

Sanfoundry Global Education & Learning Series – Electromagnetic Theory.
To practice all areas of Electromagnetic Theory, here is complete set of 1000+ Multiple Choice Questions and Answers.

advertisement
advertisement
Subscribe to our Newsletters (Subject-wise). Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Youtube | Telegram | LinkedIn | Instagram | Facebook | Twitter | Pinterest
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

Subscribe to his free Masterclasses at Youtube & technical discussions at Telegram SanfoundryClasses.