Description : Find the value of divergence theorem for the field D = 2xy i + x 2 j for the rectangular parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3. a) 10 b) 12 c) 14 d) 16
Last Answer : b) 12
Description : Find the divergence theorem value for the function given by (e z , sin x, y 2 ) a) 1 b) 0 c) -1 d) 2
Last Answer : b) 0
Description : If a function is described by F = (3x + z, y 2 − sin x 2 z, xz + ye x5 ), then the divergence theorem value in the region 0
Last Answer : c) 39
Description : Find the value of divergence theorem for A = xy 2 i + y 3 j + y 2 z k for a cuboid given by 0
Last Answer : c) 5/3
Description : 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 4π 2 m. a) 1 b) 2 c) 3 d) 4
Last Answer : b) 2
Description : Divergence theorem computes to zero for a solenoidal function. State True/False. a) True b) False
Last Answer : a) True
Description : The divergence theorem for a surface consisting of a sphere is computed in which coordinate system? a) Cartesian b) Cylindrical c) Spherical d) Depends on the function
Last Answer : d) Depends on the function
Description : When a vector is irrotational, which condition holds good? a) Stoke’s theorem gives non-zero value b) Stoke’s theorem gives zero value c) Divergence theorem is invalid d) Divergence theorem is valid
Last Answer : b) Stoke’s theorem gives zero value
Description : Find the value of Stoke’s theorem for A = x i + y j + z k. The state of the function will be a) Solenoidal b) Divergent c) Rotational d) Curl free
Last Answer : d) Curl free
Description : The Ampere law is based on which theorem? a) Green’s theorem b) Gauss divergence theorem c) Stoke’s theorem d) Maxwell theorem
Last Answer : c) Stoke’s theorem
Description : Divergence theorem is based on a) Gauss law b) Stoke’s law c) Ampere law d) Lenz law
Last Answer : a) Gauss law
Description : The Gauss divergence theorem converts a) line to surface integral b) line to volume integral c) surface to line integral d) surface to volume integral
Last Answer : d) surface to volume integral
Description : Gauss theorem uses which of the following operations? a) Gradient b) Curl c) Divergence d) Laplacian
Last Answer : c) Divergence
Description : The Green’s theorem can be related to which of the following theorems mathematically? a) Gauss divergence theorem b) Stoke’s theorem c) Euler’s theorem d) Leibnitz’s theorem
Last Answer : b) Stoke’s theorem
Description : Which of the following theorem convert line integral to surface integral? a) Gauss divergence and Stoke’s theorem b) Stoke’s theorem only c) Green’ s theorem only d) Stoke’s and Green’s theorem
Last Answer : d) Stoke’s and Green’s theorem
Description : The Stoke’s theorem uses which of the following operation? a) Divergence b) Gradient c) Curl d) Laplacian
Last Answer : c) Curl
Description : Compute divergence theorem for D = 5r 2 /4 i in spherical coordinates between r = 1 and r = 2 in volume integral. a) 80 π b) 5 π c) 75 π d) 85 π
Last Answer : c) 75 π
Description : The divergence theorem converts a) Line to surface integral b) Surface to volume integral c) Volume to line integral d) Surface to line integral
Last Answer : b) Surface to volume integral
Description : The ultimate result of the divergence theorem evaluates which one of the following? a) Field intensity b) Field density c) Potential d) Charge and flux
Last Answer : d) Charge and flux
Description : Compute divergence theorem for D= 5r 2 /4 i in spherical coordinates between r=1 and r=2. a) 80π b) 5π c) 75π d) 85π
Last Answer : c) 75π
Description : Which of the following theorem use the curl operation? a) Green’s theorem b) Gauss Divergence theorem c) Stoke’s theorem d) Maxwell equation
Last Answer : b) Gauss Divergence theorem
Description : Find the value of Stoke’s theorem for y i + z j + x k. a) i + j b) j + k c) i + j + k d) –i – j – k
Last Answer : d) –i – j – k
Description : Given D = e -x sin y i – e -x cos y j Find divergence of D. a) 3 b) 2 c) 1 d) 0
Last Answer : d) 0
Description : The divergence of distance vector is a) 0 b) 3 c) 2 d) 1
Last Answer : b) 3
Description : Find the divergence of the field, P = x 2 yz i + xz k a) xyz + 2x b) 2xyz + x c) xyz + 2z d) 2xyz + z
Last Answer : b) 2xyz + x
Description : Find the value of Green’s theorem for F = x 2 and G = y 2 is a) 0 b) 1 c) 2 d) 3
Last Answer : a) 0
Description : Find the divergence of the vector F= xe -x i + y j – xz k a) (1 – x)(1 + e -x ) b) (x – 1)(1 + e -x ) c) (1 – x)(1 – e) d) (x – 1)(1 – e)
Last Answer : a) (1 – x)(1 + e -x )
Description : The Stoke’s theorem can be used to find which of the following? a) Area enclosed by a function in the given region b) Volume enclosed by a function in the given region c) Linear distance d) Curl of the function
Last Answer : a) Area enclosed by a function in the given region
Description : Calculate the Green’s value for the functions F = y 2 and G = x 2 for the region x = 1 and y = 2 from origin. a) 0 b) 2 c) -2 d) 1
Last Answer : c) -2
Description : Divergence of gradient of a vector function is equivalent to a) Laplacian operation b) Curl operation c) Double gradient operation d) Null vector
Last Answer : a) Laplacian operation
Description : Find the Gauss value for a position vector in Cartesian system from the origin to one unit in three dimensions. a) 0 b) 3 c) -3 d) 1
Description : In the medium of free space, the divergence of the electric flux density will be a) 1 b) 0 c) -1 d) Infinity
Description : The divergence of H will be a) 1 b) -1 c) ∞ d) 0
Description : Determine the divergence of F = 30 i + 2xy j + 5xz 2 k at (1,1,-0.2) and state the nature of the field. a) 1, solenoidal b) 0, solenoidal c) 1, divergent d) 0, divergent
Last Answer : b) 0, solenoidal
Description : Find the divergence of the vector yi + zj + xk. a) -1 b) 0 c) 1 d) 3
Description : Compute the divergence of the vector xi + yj + zk. a) 0 b) 1 c) 2 d) 3
Last Answer : d) 3
Description : In a dipole, the Gauss theorem value will be a) 1 b) 0 c) -1 d) 2
Description : Find the Laplace equation value of the following potential field V = x 2 – y 2 + z 2 a) 0 b) 2 c) 4 d) 6
Description : Calculate the charge density for the current density given 20sin x i + ycos z j at the origin. a) 20t b) 21t c) 19t d) -20t
Last Answer : b) 21t
Description : The non existence of the magnetic monopole is due to which operation? a) Gradient b) Divergence c) Curl d) Laplacian
Last Answer : b) Divergence
Description : The charge density of a electrostatic field is given by a) Curl of E b) Divergence of E c) Curl of D d) Divergence of D
Last Answer : d) Divergence of D
Description : Ampere law states that, a) Divergence of H is same as the flux b) Curl of D is same as the current c) Divergence of E is zero d) Curl of H is same as the current density
Last Answer : d) Curl of H is same as the current density
Description : The divergence of which quantity will be zero? a) E b) D c) H d) B
Last Answer : d) B
Description : Identify the nature of the field, if the divergence is zero and curl is also zero. a) Solenoidal, irrotational b) Divergent, rotational c) Solenoidal, irrotational d) Divergent, rotational
Last Answer : c) Solenoidal, irrotational
Description : Find whether the vector is solenoidal, E = yz i + xz j + xy k a) Yes, solenoidal b) No, non-solenoidal c) Solenoidal with negative divergence d) Variable divergence
Last Answer : a) Yes, solenoidal
Description : The divergence concept can be illustrated using Pascal’s law. State True/False. a) True b) False
Description : The divergence of a vector is a scalar. State True/False. a) True b) False
Description : A field has zero divergence and it has curls. The field is said to be a) Divergent, rotational b) Solenoidal, rotational c) Solenoidal, irrotational d) Divergent, irrotational
Last Answer : b) Solenoidal, rotational
Description : A vector is said to be solenoidal when its a) Divergence is zero b) Divergence is unity c) Curl is zero d) Curl is unity
Last Answer : a) Divergence is zero