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Find the electric field intensity of two charges 2C and -1C separated by a distance 1m in air.
Answer: b Explanation: F = q1q2/(4∏εor2) = -2 X 9/(10-9 X 12) = -18 X 109 E = F/q = 18 X 109 /2 = 9 X 109 .
Answer: b
Explanation: F = q1q2/(4∏εor2) = -2 X 9/(10-9 X 12) = -18 X 109
E = F/q = 18 X 109
/2 = 9 X 109
.
See lessThe divergence theorem value for the function x2 + y2 + z2 at a distance of one unit from the origin is
Answer: d Explanation: Div (F) = 2x + 2y + 2z. The triple integral of the divergence of the function is ∫∫∫(2x + 2y + 2z)dx dy dz, where x = 0->1, y = 0->1 and z = 0->1. On integrating, we get 3 units.
Answer: d
Explanation: Div (F) = 2x + 2y + 2z. The triple integral of the divergence of the function is
∫∫∫(2x + 2y + 2z)dx dy dz, where x = 0->1, y = 0->1 and z = 0->1. On integrating, we get 3
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 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 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 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 lessFind 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 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 less