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Answer: d
Explanation: The curl of y i + z j + x k is i(01) – j(10) + k(01) =
i –j –k. Since the curl is zero, the value of Stoke’s theorem is zero. The function is said to be irrotational.
Answer: c
Explanation: ∫A.dl = ∫∫ Curl (A).ds is the expression for Stoke’s theorem. It is clear that the theorem uses curl operation.
Which of the following theorem convert line integral to surface integral?
Answer: d
Explanation: The Stoke’s theorem is given by ∫A.dl = ∫∫ Curl (A).ds. Green’s theorem is given by, ∫ F dx + G dy = ∫∫ (dG/dx – dF/dy) dx dy. It is clear that both the theorems convert line to surface integral.
Find the value of Stoke’s theorem for A = x i + y j + z k. The state of the function will be
Answer: Since curl is required, we need not bother about divergence property. The curl of the function will be i(00) – j(00) + k(00) = 0. The curl is zero, thus the function is said to be irrotational or curl free.
The Stoke’s theorem can be used to find which of the following?
Answer: a
Explanation: It states that the line integral of a function gives the surface area of the function enclosed by the given region. This is computed using the double integral of the curl of the function.
Answer: d
Explanation: From Stoke’s theorem, we can calculate energy stored in an inductor as 0.5Li^{2}. E = 0.5 X 2 X 4^{2} = 16 units.
Answer: a
Explanation: We can compute the energy stored in a capacitor from Stoke’s theorem as 0.5Cv^{2}. Thus given energy is 0.5 X 12 X v^{2}. We get v = 0.57 volts.
Find the power, given energy E = 2J and current density J = x^{2} 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∫ x^{2} dx as x = 0>1. We get P = 2/3 units.
The 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.
The resistivity of a material with resistance 200 ohm, length 10m and area twice that of the length is
Answer: c
Explanation: Resistance calculated from Ohm’s law and Stoke’s theorem will be R = ρL/A. To get resistivity, ρ = RA/L = 200 X 20/10 = 400.
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