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The gradient of xi + yj + zk is
Answer: d Explanation: Grad (xi + yj + zk) = 1 + 1 + 1 = 3. In other words, the gradient of any position vector is 3.
Answer: d
See lessExplanation: Grad (xi + yj + zk) = 1 + 1 + 1 = 3. In other words, the gradient of any
position vector is 3.
Divergence of gradient of a vector function is equivalent to
Answer: a 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.
Answer: a
See lessExplanation: 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.
The mathematical perception of the gradient is said to be
Answer: c Explanation: The gradient is the rate of change of space of flux in electromagnetics. This is analogous to the slope in mathematics.
Answer: c
See lessExplanation: The gradient is the rate of change of space of flux in electromagnetics. This is analogous to the slope in mathematics.
Gradient of a function is a constant. State True/False.
Answer: b 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.
Answer: b
See lessExplanation: 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.
Transform the vector (4,-2,-4) at (1,2,3) into spherical coordinates.
Answer: b Explanation: r = √(x2+y2+z2) = 3.74 Θ = cos-1(z/r) = cos-1(3/3.74) = 36.7⁰ Φ = tan-1(y/x) = tan-1(2/1) = 63.4⁰ A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sinθ)j (-4 sin φ – 2 cos φ)k On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.
Answer: b
Explanation: r = √(x2+y2+z2) = 3.74
Θ = cos-1(z/r) = cos-1(3/3.74) = 36.7⁰
Φ = tan-1(y/x) = tan-1(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sinθ)j (-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.
See lessThe scalar factor of spherical coordinates is
Answer: a Explanation: The radius varies from unity to infinity, the plane angle from zero to 360⁰ and the z plane from (-∞, ∞) .
Answer: a
See lessExplanation: The radius varies from unity to infinity, the plane angle from zero to 360⁰ and the z plane from (-∞, ∞) .
Given B= (10/r)i+( rcos θ) j+k in spherical coordinates. Find Cartesian points at (-3,4,0)
Answer: a Explanation: r = √(x2+y2+z2) = √25 = 5 Θ = cos-1(z/r) = 1 Φ = tan-1(y/x) = tan-1(-4/3) Thus, B = -2i + j.
Answer: a
Explanation: r = √(x2+y2+z2) = √25 = 5
Θ = cos-1(z/r) = 1
Φ = tan-1(y/x) = tan-1(-4/3)
Thus, B = -2i + j.
See lessThe area of sphere can be computed from the sphere volume. State True/False.
Answer: a Explanation: On double integrating the differential volume, the area can be computed for a sphere.
Answer: a
See lessExplanation: On double integrating the differential volume, the area can be computed for a sphere.
Find the Cartesian coordinates of B(4,25⁰,120⁰)
Answer: b Explanation: x = r sin θ cos φ = 4 sin25⁰ cos 120⁰ = -0.845 y = r sin θ sin φ = 4 sin 25⁰ sin 120⁰ = 1.462 z = r cos θ = 4 cos 25⁰ = 3.625.
Answer: b
See lessExplanation: x = r sin θ cos φ = 4 sin25⁰ cos 120⁰ = -0.845
y = r sin θ sin φ = 4 sin 25⁰ sin 120⁰ = 1.462
z = r cos θ = 4 cos 25⁰ = 3.625.
Find the spherical coordinates of A(2,3,-1)
Answer: b Explanation: r = √(x2+y2+z2) = √14 = 3.74 Θ = cos-1(z/r) = cos-1(-1/3.74) = 105.5⁰ Φ = tan-1(y/x) = tan-1(3/2) = 56.31⁰.
Answer: b
Explanation: r = √(x2+y2+z2) = √14 = 3.74
Θ = cos-1(z/r) = cos-1(-1/3.74) = 105.5⁰
Φ = tan-1(y/x) = tan-1(3/2) = 56.31⁰.
See less