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NIMCET 2024 Paper

Section: Mathematics

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Question : 41 of 120

Marks: +1, -0

The vector

\overset{\rightarrow}{A}=(2x+1)\hat{i}+(x^2-6y)\hat{j}+(xy^2+3z)\hat{k}

Sink field
Solenoidal field
Source field
None of these

Solution:

The divergence of the vector

\overline{A}

is given bu

\div(\overline{A})=\frac{\partial A_x}{\partial x}+\frac{\partial A_y}{\partial y}+\frac{\partial A_z}{\partial z}

Here

A_x=2x+1,\;A_y=x^2-6y,\;A_z=xy^2+3z

Hence

\div(\overline{A})=2-6+3=-1

If

\div(\overline{A})>0

, the field is a source field.

If

\div(\overline{A})<0

, the field is a sink field.

If

\div(\overline{A})=0

, the field is a solenoidal field.

Since

\div(\overline{A})=-1

, the vector field is a sink field.

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