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Identify the nature of the field, if the divergence is zero and curl is also zero.
- a)Solenoidal, irrotational
- b)Divergent, rotational
- c)Solenoidal, irrotational
- d)Divergent, rotational
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Identify the nature of the field, if the divergence is zero and curl i...
Since the vector field does not diverge (moves in a straight path), the divergence is zero. Also, the path does not possess any curls, so the field is irrotational.
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Hence option (C) is correct
To learn more about Divergence and Curl of a vector click on the link given below:
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Identify the nature of the field, if the divergence is zero and curl i...
Nature of Field with Zero Divergence and Zero Curl
The nature of the field can be determined by analyzing the divergence and curl of the field. If the divergence of the field is zero and the curl of the field is also zero, then the field can be classified as solenoidal and irrotational. Let's understand the terms solenoidal and irrotational in detail:
1. Solenoidal Field: A field is said to be solenoidal if it has zero divergence. This means that the net flow of the field across any closed surface is zero. In other words, the field is incompressible and has no sources or sinks. Examples of solenoidal fields include the magnetic field around a current-carrying wire and the velocity field of an incompressible fluid.
2. Irrotational Field: A field is said to be irrotational if it has zero curl. This means that the field has no vortices or rotational components. In other words, the field is conservative and can be expressed as the gradient of a scalar potential. Examples of irrotational fields include the electric field around a point charge and the gravitational field around a point mass.
Therefore, if a field has zero divergence and zero curl, it can be classified as both solenoidal and irrotational. This implies that the field is both incompressible and conservative, and can be represented as the gradient of a scalar potential. Such fields are commonly encountered in fluid mechanics, electromagnetism, and other areas of physics and engineering.
The nature of the field can be determined by analyzing the divergence and curl of the field. If the divergence of the field is zero and the curl of the field is also zero, then the field can be classified as solenoidal and irrotational. Let's understand the terms solenoidal and irrotational in detail:
1. Solenoidal Field: A field is said to be solenoidal if it has zero divergence. This means that the net flow of the field across any closed surface is zero. In other words, the field is incompressible and has no sources or sinks. Examples of solenoidal fields include the magnetic field around a current-carrying wire and the velocity field of an incompressible fluid.
2. Irrotational Field: A field is said to be irrotational if it has zero curl. This means that the field has no vortices or rotational components. In other words, the field is conservative and can be expressed as the gradient of a scalar potential. Examples of irrotational fields include the electric field around a point charge and the gravitational field around a point mass.
Therefore, if a field has zero divergence and zero curl, it can be classified as both solenoidal and irrotational. This implies that the field is both incompressible and conservative, and can be represented as the gradient of a scalar potential. Such fields are commonly encountered in fluid mechanics, electromagnetism, and other areas of physics and engineering.
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Identify the nature of the field, if the divergence is zero and curl i...
C
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Identify the nature of the field, if the divergence is zero and curl is also zero.a)Solenoidal, irrotationalb)Divergent, rotationalc)Solenoidal, irrotationald)Divergent, rotationalCorrect answer is option 'C'. Can you explain this answer?
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