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A vector field which has a vanishing divergence is called as ____________
- a)Rotational field
- b)Hemispheroidal field
- c)Solenoidal field
- d)Irrotational field
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A vector field which has a vanishing divergence is called as _________...
By the definition: A vector field whose divergence comes out to be zero or Vanishes is called as a Solenoidal Vector Field.
i.e.
Most Upvoted Answer
A vector field which has a vanishing divergence is called as _________...
By the definition: A vector field whose divergence comes out to be zero or Vanishes is called as a Solenoidal Vector Field.
i.e.
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A vector field which has a vanishing divergence is called as _________...
Explanation:
Solenoidal Field:
- A vector field is called a solenoidal field if its divergence is zero.
- Mathematically, a vector field F is solenoidal if div(F) = 0.
- Solenoidal fields represent the flow of a fluid that is incompressible, where the fluid cannot be created or destroyed within the flow.
- In other words, the solenoidal field describes a flow where the fluid lines are diverging or converging, but the total flow of fluid into or out of any region is zero.
Vanishing Divergence:
- The term "vanishing divergence" simply means that the divergence of the vector field is zero at every point in space.
- For a solenoidal field, the divergence is always zero, indicating that there is no net flow of the field out of any closed surface in space.
- This property is essential in various physical phenomena, such as fluid dynamics, electromagnetism, and quantum mechanics.
Applications:
- Solenoidal fields find applications in fluid dynamics, where they represent the flow of incompressible fluids.
- In electromagnetism, solenoidal fields are crucial for describing the behavior of magnetic fields in a region without magnetic monopoles.
- In quantum mechanics, solenoidal fields are used to describe the wave functions of particles in stationary states.
Conclusion:
- In conclusion, a vector field with a vanishing divergence is termed as a solenoidal field, which plays a significant role in various physical phenomena due to its incompressible and divergence-free nature.
Solenoidal Field:
- A vector field is called a solenoidal field if its divergence is zero.
- Mathematically, a vector field F is solenoidal if div(F) = 0.
- Solenoidal fields represent the flow of a fluid that is incompressible, where the fluid cannot be created or destroyed within the flow.
- In other words, the solenoidal field describes a flow where the fluid lines are diverging or converging, but the total flow of fluid into or out of any region is zero.
Vanishing Divergence:
- The term "vanishing divergence" simply means that the divergence of the vector field is zero at every point in space.
- For a solenoidal field, the divergence is always zero, indicating that there is no net flow of the field out of any closed surface in space.
- This property is essential in various physical phenomena, such as fluid dynamics, electromagnetism, and quantum mechanics.
Applications:
- Solenoidal fields find applications in fluid dynamics, where they represent the flow of incompressible fluids.
- In electromagnetism, solenoidal fields are crucial for describing the behavior of magnetic fields in a region without magnetic monopoles.
- In quantum mechanics, solenoidal fields are used to describe the wave functions of particles in stationary states.
Conclusion:
- In conclusion, a vector field with a vanishing divergence is termed as a solenoidal field, which plays a significant role in various physical phenomena due to its incompressible and divergence-free nature.
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A vector field which has a vanishing divergence is called as ____________a)Rotational fieldb)Hemispheroidal fieldc)Solenoidal fieldd)Irrotational fieldCorrect answer is option 'C'. Can you explain this answer?
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