NIMCET 2024 — Mathematics PYQ
NIMCET | Mathematics | 2024The vector A=(2x+1)i^+(x2−6y)j^+(xy2+3z)k^ is a
Choose the correct answer:
- A.
sink field
(Correct Answer) - B.
solenoidal field
- C.
source field
- D.
None of these
sink field
Explanation
A=(2x+1)i^+(x2−6y)j^+(xy2+3z)k^
∇⋅A=0⇒ Solenoidal
\nabla \cdot \vec{A} < 0 \Rightarrow Sink
\nabla \cdot \vec{A} > 0 \Rightarrow Source
∇⋅A=(∂x∂i^+∂y∂j^+∂z∂k^)⋅((2x+1)i^+(x2−6y)j^+(xy2+3z)k^)
=∂x∂(2x+1)+∂y∂(x2−6y)+∂z∂(xy2+3z)
=2−6+3=−1 (negative ⇒ Sink)
Explanation
A=(2x+1)i^+(x2−6y)j^+(xy2+3z)k^
∇⋅A=0⇒ Solenoidal
\nabla \cdot \vec{A} < 0 \Rightarrow Sink
\nabla \cdot \vec{A} > 0 \Rightarrow Source
∇⋅A=(∂x∂i^+∂y∂j^+∂z∂k^)⋅((2x+1)i^+(x2−6y)j^+(xy2+3z)k^)
=∂x∂(2x+1)+∂y∂(x2−6y)+∂z∂(xy2+3z)
=2−6+3=−1 (negative ⇒ Sink)