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Find the value of Green’s theorem for F = x2 and G = y2 is
Answer: a Explanation: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(0 – 0)dx dy = 0. The value of Green’s theorem gives zero for the functions given.
Answer: a
Explanation: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(0 – 0)dx dy = 0. The value of Green’s theorem
gives zero for the functions given.
See lessWhich of the following is not an application of Green’s theorem?
Answer: c Explanation: In physics, Green’s theorem is used to find the two dimensional flow integrals. In plane geometry, it is used to find the area and centroid of plane figures.
Answer: c
Explanation: In physics, Green’s theorem is used to find the two dimensional flow
integrals. In plane geometry, it is used to find the area and centroid of plane figures.
See lessThe path traversal in calculating the Green’s theorem is
Answer: b Explanation: The Green’s theorem calculates the area traversed by the functions in the region in the anticlockwise direction. This converts the line integral to surface integral.
Answer: b
Explanation: The Green’s theorem calculates the area traversed by the functions in the
region in the anticlockwise direction. This converts the line integral to surface integral.
See lessCalculate the Green’s value for the functions F = y2 and G = x2 for the region x = 1 and y = 2 from origin.
Answer: c Explanation: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(2x – 2y)dx dy. On integrating for x = 0->1 and y = 0->2, we get Green’s value as -2.
Answer: c
Explanation: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(2x – 2y)dx dy. On integrating for x = 0->1 and y
= 0->2, we get Green’s value as -2.
See lessFind 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
Explanation: (Del)2
(r cos θ + φ) = (2 cosθ/r) – (2 cosθ/r) + 0
= 0, this satisfies Laplace equation. This value is 0.
See lessThe 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
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 equation will not employ Laplacian operator.
See lessWhen 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
Explanation: A field satisfying the Laplace equation is termed as harmonic field.
See lessWhich 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
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.
See lessCompute the Gauss law for D = 10ρ3 /4 i, in cylindrical coordinates with ρ = 4m, z = 0 and z = 5, hence find charge using volume integral.
Answer: d Explanation: Q = D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed. The divergence of D given is, Div(D) = 10 ρ2 and dv = ρ dρ dφ dz. On integrating, ρ = 0- >4, φ = 0->2π and z = 0->5, we get Q = 6400 π
Answer: d
Explanation: Q = D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.
The divergence of D given is, Div(D) = 10 ρ2 and dv = ρ dρ dφ dz. On integrating, ρ = 0-
>4, φ = 0->2π and z = 0->5, we get Q = 6400 π
See lessUsing volume integral, which quantity can be calculated?
Answer: c Explanation: The volume integral gives the volume of a vector in a region. Thus volume of a cube can be computed.
Answer: c
Explanation: The volume integral gives the volume of a vector in a region. Thus volume
of a cube can be computed.
See less