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The Stoke’s theorem can be used to find which of the following?
Answer: a Explanation: It states that the line integral of a function gives the surface area of the function enclosed by the given region. This is computed using the double integral of the curl of the function.
Answer: a
See lessExplanation: It states that the line integral of a function gives the surface area of the
function enclosed by the given region. This is computed using the double integral of the curl of the function.
Find the value of Stoke’s theorem for A = x i + y j + z k. The state of the function will be
Answer: d Explanation: Since curl is required, we need not bother about divergence property. The curl of the function will be i(0-0) – j(0-0) + k(0-0) = 0. The curl is zero, thus the function is said to be irrotational or curl free.
Answer: d
See lessExplanation: Since curl is required, we need not bother about divergence property. The curl of the function will be i(0-0) – j(0-0) + k(0-0) = 0. The curl is zero, thus the function is said to be irrotational or curl free.
Which of the following theorem convert line integral to surface integral?
Answer: d Explanation: The Stoke’s theorem is given by ∫A.dl = ∫∫ Curl (A).ds. Green’s theorem is given by, ∫ F dx + G dy = ∫∫ (dG/dx – dF/dy) dx dy. It is clear that both the theorems convert line to surface integral.
Answer: d
See lessExplanation: The Stoke’s theorem is given by ∫A.dl = ∫∫ Curl (A).ds. Green’s theorem is given by, ∫ F dx + G dy = ∫∫ (dG/dx – dF/dy) dx dy. It is clear that both the theorems convert line to surface integral.
The Stoke’s theorem uses which of the following operation?
Answer: c Explanation: ∫A.dl = ∫∫ Curl (A).ds is the expression for Stoke’s theorem. It is clear that the theorem uses curl operation.
Answer: c
See lessExplanation: ∫A.dl = ∫∫ Curl (A).ds is the expression for Stoke’s theorem. It is clear that the theorem uses curl operation.
Find the value of Stoke’s theorem for y i + z j + x k.
Answer: d Explanation: The curl of y i + z j + x k is i(0-1) – j(1-0) + k(0-1) = -i –j –k. Since the curl is zero, the value of Stoke’s theorem is zero. The function is said to be irrotational.
Answer: d
See lessExplanation: The curl of y i + z j + x k is i(0-1) – j(1-0) + k(0-1) =
-i –j –k. Since the curl is zero, the value of Stoke’s theorem is zero. The function is said to be irrotational.
When a potential satisfies Laplace equation, then it is said to be
Answer: d Explanation: A field satisfying the Laplace equation is termed as harmonic field.
Answer: d
See lessExplanation: A field satisfying the Laplace equation is termed as harmonic field.
The Laplacian operator cannot be used in which one the following?
Answer: d Explanation: Poisson equation, two-dimensional heat and wave equations are general cases of Laplacian equation. Maxwell equation uses only divergence and curl, which is first order differential equation, whereas Laplacian operator is second order differential equation. Thus Maxwell equatioRead more
Answer: d
See lessExplanation: Poisson equation, two-dimensional heat and wave equations are general
cases of Laplacian equation. Maxwell equation uses only divergence and curl, which is
first order differential equation, whereas Laplacian operator is second order differential equation. Thus Maxwell equation will not employ Laplacian operator.
Find the Laplace equation value of the following potential field V = r cos θ + φ
Answer: d Explanation: (Del)2 (r cos θ + φ) = (2 cosθ/r) – (2 cosθ/r) + 0 = 0, this satisfies Laplace equation. This value is 0.
Answer: d
See lessExplanation: (Del)2 (r cos θ + φ) = (2 cosθ/r) – (2 cosθ/r) + 0
= 0, this satisfies Laplace equation. This value is 0.
Find the Laplace equation value of the following potential field V = ρ cosφ + z
Answer: a Explanation: (Del)2(ρ cosφ + z)= (cos φ/r) – (cos φ/r) + 0 = 0, this satisfies Laplace equation. The value is 0.
Answer: a
See lessExplanation: (Del)2(ρ cosφ + z)= (cos φ/r) – (cos φ/r) + 0
= 0, this satisfies Laplace equation. The value is 0.
Find the Laplace equation value of the following potential field V = x2 – y 2 + z2
Answer: b Explanation: (Del) V = 2x – 2y + 2z (Del)2 V = 2 – 2 + 2= 2, which is non zero value. Thus it doesn’t satisfy Laplace equation
Answer: b
See lessExplanation: (Del) V = 2x – 2y + 2z
(Del)2 V = 2 – 2 + 2= 2, which is non zero value. Thus it doesn’t satisfy Laplace
equation