A vector field𝐁(𝑥, 𝑦, 𝑧) = 𝑥 𝑖̂ + 𝑦 ĵ − 2𝑧 k̂is defined over a conical region having height ℎ = 2, base radius 𝑟 = 3 and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin.If 𝒏 denotes the unit outward normal to the curved surface 𝑆 of the cone, the value of the integral ∫ _{S}B.n dS equals _________ . (Answer in integer)

Question

A vector field𝐁(𝑥, 𝑦, 𝑧) = 𝑥 𝑖̂ + 𝑦 ĵ − 2𝑧 k̂is defined over a conical region having height ℎ = 2, base radius 𝑟 = 3 and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin.If 𝒏 denotes the unit outward normal to the curved surface 𝑆 of the cone, the value of the integral ∫  _{S}B.n dS equals _________ . (Answer in integer)

Examsnet · Accepted Answer

Correct Answer is : -0.001-0.001

GATE Mechanical Engineering (ME) 2023 Shift 1 Solved Paper