The figures show diagramatic representations of vector fields- X-Y- and Z- respectively- Which one of the following choices is true-

From the given figures we can observe that: Fig (1):X⃗ is diverging field hence its divergence of X i.e. ▽ .X⃗≠ 0. Fig (2):Y⃗ is circularly rotating field hence ...

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Engineering Mathematics

Divergence and Curl

The figures s...

Question

The figures show diagramatic representations of vector fields, $\to X, \to Y$ and $\to Z$ , respectively. Which one of the following choices is true?

▽ . \to X = 0, ▽ \times \to Y \neq 0, ▽ \times \to Z = 0

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▽ . \to X \neq 0, ▽ \times \to Y = 0, ▽ \times \to Z \neq 0

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▽ . \to X \neq 0, ▽ \times \to Y \neq 0, ▽ \times \to Z \neq 0

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▽ . \to X = 0, ▽ \times \to Y = 0, ▽ \times \to Z = 0

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Solution

The correct option is C $▽ . \to X \neq 0, ▽ \times \to Y \neq 0, ▽ \times \to Z \neq 0$
From the given figures we can observe that:
Fig $(1) : \to X$ is diverging field hence its divergence of $X$
$i . e . ▽ . \to X \neq 0.$
Fig $(2) : \to Y$ is circularly rotating field hence its curl of $Y i . e . ▽ \times \to Y \neq 0.$
Fig $(3) : \to Z$ is also ca circularly rotating field hence its curl of $Z i . e . ▽ \times \to Z \neq 0.$
Hence , option (c) satisfies the above three conditions

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The figures show diagramatic representations of vector fields, →X,→Y and →Z, respectively. Which one of the following choices is true?

The figures show diagramatic representations of vector fields, $\to X, \to Y$ and $\to Z$ , respectively. Which one of the following choices is true?