Given a function ϕ = 1/2(x2 + y2 + z2) in three-dimensional Cartesian space, the value of the surface integral ∯S n̂ . ∇ϕ dS where S is the surface of a sphere of unit radius and n̂ is the outward unit normal vector on S, is
The value of where S is the surface of unit sphere x2 + y2 + z2 = 1 is
1 Crore+ students have signed up on EduRev. Have you? Download the App |
Consider a closed surface S surrounding volume V. If is the position vector of a point inside S, with the unit normal on S, the value of the integral is
Find the value of ds where and S is the surface of sphere x2 + y2 + z2 = 16 ____
The divergence theorem for a surface consisting of a sphere is computed in which coordinate system?
The divergence theorem value for the function x2 + y2 + z2 at a distance of one unit from the origin is
For a function given by F = 4x i + 7y j +z k, the divergence theorem evaluates to which of the values given, if the surface considered is a cone of radius 1/2π m and height 4π2 m.
Find the divergence theorem value for the function given by (ez, sin x, y2)
The value of the surface integral over the surface S of the sphere x2 + y2 + z2 = 9, where n is the unit outward normal to the surface element dS, is _______.
The value of ∯ (4xî - 2y2j + z2k).n̂ds where S is bounded by x2 + y2 = 4, Z = 0 and Z = 3 is
Identify the nature of the field, if the divergence is zero and curl is also zero.
Find whether the vector is solenoidal, E = yz i + xz j + xy k
65 videos|120 docs|94 tests
|
65 videos|120 docs|94 tests
|