एक सदिश को सोलेनॉइडल (solenoidal) कहा जाता है जब उसका
उत्तर और चरणबद्ध हल
सोलेनॉइडल सदिश क्षेत्र अपसरण-मुक्त होता है: ∇·A = 0। भौतिक रूप से, क्षेत्र के भीतर कोई शुद्ध स्रोत या सिंक नहीं होता।
विस्तृत हल (मूल भाषा में)
Concept & Reasoning
Divergence measures the local net outward flux density of a vector field. If divergence is zero everywhere in a region, the field is called solenoidal. Magnetic flux density B is a classic example because ∇·B=0 expresses the absence of magnetic monopoles. Curl is a different operator that measures local rotation and does not define solenoidality.
How to Solve It in the Exam
Solenoidal = divergence zero; irrotational = curl zero.
Important Exam Point
Pair the two vocabulary words with the correct vector operator.
Quick Trick
Solenoidal = divergence zero; irrotational = curl zero.
Common Mistake
Do not confuse solenoidal with curl-free; a field can be divergence-free and still have nonzero curl.
A vector is said to be solenoidal when its
Answer & step-by-step solution
A solenoidal vector field is divergence-free: ∇·A = 0. Physically, it has no net source or sink within the region.
Concept & Reasoning
Divergence measures the local net outward flux density of a vector field. If divergence is zero everywhere in a region, the field is called solenoidal. Magnetic flux density B is a classic example because ∇·B=0 expresses the absence of magnetic monopoles. Curl is a different operator that measures local rotation and does not define solenoidality.
How to Solve It in the Exam
Solenoidal = divergence zero; irrotational = curl zero.
Important Exam Point
Pair the two vocabulary words with the correct vector operator.
Quick Trick
Solenoidal = divergence zero; irrotational = curl zero.
Common Mistake
Do not confuse solenoidal with curl-free; a field can be divergence-free and still have nonzero curl.
સદિશને સોલેનોઇડલ (solenoidal) કહેવાય છે જ્યારે તેનું
જવાબ અને પગલાવાર ઉકેલ
સોલેનોઇડલ સદિશ ક્ષેત્ર અપસરણ-મુક્ત હોય છે: ∇·A = 0. ભૌતિક રીતે, વિસ્તારમાં કોઈ ચોખ્ખો સ્રોત કે સિંક હોતો નથી.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Concept & Reasoning
Divergence measures the local net outward flux density of a vector field. If divergence is zero everywhere in a region, the field is called solenoidal. Magnetic flux density B is a classic example because ∇·B=0 expresses the absence of magnetic monopoles. Curl is a different operator that measures local rotation and does not define solenoidality.
How to Solve It in the Exam
Solenoidal = divergence zero; irrotational = curl zero.
Important Exam Point
Pair the two vocabulary words with the correct vector operator.
Quick Trick
Solenoidal = divergence zero; irrotational = curl zero.
Common Mistake
Do not confuse solenoidal with curl-free; a field can be divergence-free and still have nonzero curl.
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