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If a function is described by F = (3x + z, y2 − sin x2z, xz + yex5), then the divergence theorem value in the region 0<x<1, 0<y<3 and 0<z<2 will be
Answer: c Explanation: Div (F) = 3 + 2y + x. By divergence theorem, the triple integral of Div F in the region is ∫∫∫ (3 + 2y + x) dx dy dz. On integrating from x = 0->1, y = 0->3 and z = 0- >2, we get 39 units.
Answer: c
Explanation: Div (F) = 3 + 2y + x. By divergence theorem, the triple integral of Div F in
the region is ∫∫∫ (3 + 2y + x) dx dy dz. On integrating from x = 0->1, y = 0->3 and z = 0-
>2, we get 39 units.
See lessCoulomb law is employed in
Answer: a Explanation: Coulomb law is applied to static charges. It states that force between any two point charges is proportional to the product of the charges and inversely proportional to square of the distance between them. Thus it is employed in electrostatics.
Answer: a
Explanation: Coulomb law is applied to static charges. It states that force between any
two point charges is proportional to the product of the charges and inversely proportional
to square of the distance between them. Thus it is employed in electrostatics.
See lessTwo charges 1C and -4C exists in air. What is the direction of force?
Answer: c Explanation: Since the charges are unlike, the force will be attractive. Thus the force directs from 1C to -4C.
Answer: c
Explanation: Since the charges are unlike, the force will be attractive. Thus the force
directs from 1C to -4C.
See lessApplications of Green’s theorem are meant to be in
Answer: b Explanation: Since Green’s theorem converts line integral to surface integral, we get the value as two dimensional. In other words the functions are variable with respect to x,y, which is two dimensional.
Answer: b
Explanation: Since Green’s theorem converts line integral to surface integral, we get the
value as two dimensional. In other words the functions are variable with respect to x,y,
which is two dimensional.
See lessThe Gauss divergence theorem converts
Answer: d Explanation: The divergence theorem for a function F is given by ∫∫ F.dS = ∫∫∫ Div (F).dV. Thus it converts surface to volume integral.
Answer: d
Explanation: The divergence theorem for a function F is given by ∫∫ F.dS = ∫∫∫ Div (F).dV.
Thus it converts surface to volume integral.
See lessFind the Gauss value for a position vector in Cartesian system from the origin to one unit in three dimensions.
Answer: b Explanation: The position vector in Cartesian system is given by R = x i + y j + z k. Div(R) = 1 + 1 + 1 = 3. By divergence theorem, ∫∫∫3.dV, where V is a cube with x = 0->1, y = 0->1 and z = 0->1. On integrating, we get 3 units.
Answer: b
Explanation: The position vector in Cartesian system is given by R = x i + y j + z k.
Div(R) = 1 + 1 + 1 = 3. By divergence theorem, ∫∫∫3.dV, where V is a cube with x = 0->1,
y = 0->1 and z = 0->1. On integrating, we get 3 units.
See lessThe voltage of a capacitor 12F with a rating of 2J energy is
Answer: a Explanation: We can compute the energy stored in a capacitor from Stoke’s theorem as 0.5Cv2 . Thus given energy is 0.5 X 12 X v2 . We get v = 0.57 volts.
Answer: a
Explanation: We can compute the energy stored in a capacitor from Stoke’s theorem as
0.5Cv2
. Thus given energy is 0.5 X 12 X v2
. We get v = 0.57 volts.
See lessFind the power, given energy E = 2J and current density J = x2 varies from x = 0 and x = 1.
Answer: b Explanation: From Stoke’s theorem, we can calculate P = E X I = ∫ E. J ds = 2∫ x2 dx as x = 0->1. We get P = 2/3 units.
Answer: b
Explanation: From Stoke’s theorem, we can calculate P = E X I = ∫ E. J ds
= 2∫ x2 dx as x = 0->1. We get P = 2/3 units.
See lessThe conductivity of a material with current density 1 unit and electric field 200 μV is
Answer: d Explanation: The current density is given by, J = σE. To find conductivity, σ = J/E = 1/200 X 10-6 = 5000.
Answer: d
Explanation: The current density is given by, J = σE. To find conductivity, σ = J/E =
1/200 X 10-6 = 5000.
See lessMathematically, the functions in Green’s theorem will be
Answer: c Explanation: The Green’s theorem states that if L and M are functions of (x,y) in an open region containing D and having continuous partial derivatives then, ∫ (F dx + G dy) = ∫∫(dG/dx – dF/dy)dx dy, with path taken anticlockwise.
Answer: c
Explanation: The Green’s theorem states that if L and M are functions of (x,y) in an open
region containing D and having continuous partial derivatives then,
∫ (F dx + G dy) = ∫∫(dG/dx – dF/dy)dx dy, with path taken anticlockwise.
See less