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

1. Gradient of a function is a constant. State True/False.
a) True
b) False

Explanation: Gradient of any scalar function may be defined as a vector. The vector’s magnitude and direction are those of the maximum space rate of change of φ.

2. The mathematical perception of the gradient is said to be
a) Tangent
b) Chord
c) Slope
d) Arc

Explanation: The gradient is the rate of change of space of flux in electromagnetics. This is analogous to the slope in mathematics.

3. Divergence of gradient of a vector function is equivalent to
a) Laplacian operation
b) Curl operation
d) Null vector

Explanation: Div (Grad V) = (Del)2V, which is the Laplacian operation. A function is said to be harmonic in nature, when its Laplacian tends to zero.

4. The gradient of xi + yj + zk is
a) 0
b) 1
c) 2
d) 3

Explanation: Grad (xi + yj + zk) = 1 + 1 + 1 = 3. In other words, the gradient of any position vector is 3.

5. Find the gradient of t = x2y+ ez at the point p(1,5,-2)
a) i + 10j + 0.135k
b) 10i + j + 0.135k
c) i + 0.135j + 10k
d) 10i + 0.135j + k

Explanation: Grad(t) = 2xy i + x2 j + ez k. On substituting p(1,5,-2), we get 10i + j + 0.135k.

6. Curl of gradient of a vector is
a) Unity
b) Zero
c) Null vector
d) Depends on the constants of the vector

Explanation: Gradient of any function leads to a vector. Similarly curl of that vector gives another vector, which is always zero for all constants of the vector. A zero value in vector is always termed as null vector(not simply a zero).

7. Find the gradient of the function given by, x2 + y2 + z2 at (1,1,1)
a) i + j + k
b) 2i + 2j + 2k
c) 2xi + 2yj + 2zk
d) 4xi + 2yj + 4zk

Explanation: Grad(x2+y2+z2) = 2xi + 2yj + 2zk. Put x=1, y=1, z=1, the gradient will be 2i + 2j + 2k.

8. The gradient can be replaced by which of the following?
a) Maxwell equation
b) Volume integral
c) Differential equation
d) Surface integral

Explanation: Since gradient is the maximum space rate of change of flux, it can be replaced by differential equations.

9. When gradient of a function is zero, the function lies parallel to the x-axis. State True/False.
a) True
b) False

Explanation: Gradient of a function is zero implies slope is zero. When slope is zero, the function will be parallel to x-axis or y value is constant.

10. Find the gradient of the function sin x + cos y.
a) cos x i – sin y j
b) cos x i + sin y j
c) sin x i – cos y j
d) sin x i + cos y j
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