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Find whether the vector is solenoidal, E = yz i + xz j + xy k
  • a)
    Yes, solenoidal
  • b)
    No, non-solenoidal
  • c)
    Solenoidal with negative divergence
  • d)
    Variable divergence
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find whether the vector is solenoidal, E = yz i + xz j + xy ka)Yes, so...
Answer: a
Explanation: Div(E) = Dx(yz) + Dy(xz) + Dz(xy) = 0. The divergence is zero, thus vector is divergentless or solenoidal.
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Most Upvoted Answer
Find whether the vector is solenoidal, E = yz i + xz j + xy ka)Yes, so...
Explanation:

  • Solenoidal Vector: A vector field is said to be solenoidal if its divergence is zero.

  • Divergence: The divergence of a vector field is a scalar field that measures the amount of a vector field's source or sink at a given point.

  • Given vector field is: E = yz i + xz j + xy k

  • Let's find the divergence of the given vector field E.



Finding Divergence of E:

Divergence of E = ∇.E

= ∂(yz)/∂x + ∂(xz)/∂y + ∂(xy)/∂z

= 0+0+0

= 0



  • As the divergence of the given vector field E is zero, it is a solenoidal vector.

  • Hence, option 'A' is correct.

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Find whether the vector is solenoidal, E = yz i + xz j + xy ka)Yes, solenoidalb)No, non-solenoidalc)Solenoidal with negative divergenced)Variable divergenceCorrect answer is option 'A'. Can you explain this answer?
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