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The curl of a curl of a vector gives a
Answer: b Explanation: Curl is always defined for vectors only. The curl of a vector is a vector only. The curl of the resultant vector is also a vector only.
Answer: b
See lessExplanation: Curl is always defined for vectors only. The curl of a vector is a vector only. The curl of the resultant vector is also a vector only.
Which of the following theorem use the curl operation?
Answer: c Explanation: The Stoke’s theorem is given by ∫ A.dl = ∫Curl(A).ds, which uses the curl operation. There can be confusion with Maxwell equation also, but it uses curl in electromagnetics specifically, whereas the Stoke’s theorem uses it in a generalised manner. Thus the best option is StokeRead more
Answer: c
See lessExplanation: The Stoke’s theorem is given by ∫ A.dl = ∫Curl(A).ds, which uses the curl
operation. There can be confusion with Maxwell equation also, but it uses curl in
electromagnetics specifically, whereas the Stoke’s theorem uses it in a generalised
manner. Thus the best option is Stoke’s theorem
The curl of curl of a vector is given by
Answer: b Explanation: Curl (Curl V) = Grad (Div V) – (Del)2V is a standard result of the curl operation.
Answer: b
See lessExplanation: Curl (Curl V) = Grad (Div V) – (Del)2V is a standard result of the curl
operation.
Curl is defined as the angular velocity at every point of the vector field. State True/False.
Answer: a Explanation: Curl is defined as the circulation of a vector per unit area. It is the cross product of the del operator and any vector field. Circulation implies the angular at every point of the vector field. It is obtained by multiplying the component of the vector parallel to the specifiRead more
Answer: a
See lessExplanation: Curl is defined as the circulation of a vector per unit area. It is the cross product of the del operator and any vector field. Circulation implies the angular at every point of the vector field. It is obtained by multiplying the component of the vector parallel to the specified closed path at each point along it, by the differential path length and summing the results.
Identify the nature of the field, if the divergence is zero and curl is also zero
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.
Answer: c
See lessExplanation: 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.
Find the divergence of the field, P = x2yz i + xz k
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
Answer: b
See lessExplanation: 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
Find whether the vector is solenoidal, E = yz i + xz j + xy k
Answer: a Explanation: Div(E) = Dx(yz) + Dy(xz) + Dz(xy) = 0. The divergence is zero, thus vector is divergentless or solenoidal.
Answer: a
See lessExplanation: Div(E) = Dx(yz) + Dy(xz) + Dz(xy) = 0. The divergence is zero, thus vector is divergentless or solenoidal.
Determine the divergence of F = 30 i + 2xy j + 5xz2 k at (1,1,-0.2) and state the nature of the field.
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 zRead more
Answer: b
See lessExplanation: 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.
Find the divergence of the vector F= xe-x i + y j – xz k
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).
Answer: a
See lessExplanation: 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).
Given D = e-xsin y i – e-xcos y j Find divergence of D.
Answer: d Explanation: Div (D) = Dx(e-xsin y) + Dy(-e-xcos y ) = -e-xsin y + e-xsin y = 0.
Answer: d
See lessExplanation: Div (D) = Dx(e-xsin y) + Dy(-e-xcos y ) = -e-xsin y + e-xsin y = 0.