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Divergence theorem computes to zero for a solenoidal function. State True/False.
- a)True
- b)False
Correct answer is option 'A'. Can you explain this answer?
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Divergence theorem computes to zero for a solenoidal function. State T...
Answer: a
Explanation: The divergence theorem is given by, ∫∫ F.dS = ∫∫∫ Div (F).dV, for a function F. If the function is solenoidal, its divergence will be zero. Thus the theorem computes to zero.
Explanation: The divergence theorem is given by, ∫∫ F.dS = ∫∫∫ Div (F).dV, for a function F. If the function is solenoidal, its divergence will be zero. Thus the theorem computes to zero.
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Divergence theorem computes to zero for a solenoidal function. State T...
Explanation:
The divergence theorem, also known as Gauss's theorem, relates the flow of a vector field through a closed surface to the divergence of the vector field within the surface. Mathematically, it can be written as:
∫∫S F·dS = ∫V div(F) dV
where S is a closed surface enclosing a volume V, F is a vector field, and div(F) is the divergence of F.
A solenoidal function is a vector field that has zero divergence. This means that the flow of the vector field through any closed surface is zero. Therefore, when we apply the divergence theorem to a solenoidal function, the right-hand side of the equation becomes zero.
∫∫S F·dS = ∫V div(F) dV
∫∫S F·dS = ∫V 0 dV
∫∫S F·dS = 0
Hence, the statement "Divergence theorem computes to zero for a solenoidal function" is true.
The divergence theorem, also known as Gauss's theorem, relates the flow of a vector field through a closed surface to the divergence of the vector field within the surface. Mathematically, it can be written as:
∫∫S F·dS = ∫V div(F) dV
where S is a closed surface enclosing a volume V, F is a vector field, and div(F) is the divergence of F.
A solenoidal function is a vector field that has zero divergence. This means that the flow of the vector field through any closed surface is zero. Therefore, when we apply the divergence theorem to a solenoidal function, the right-hand side of the equation becomes zero.
∫∫S F·dS = ∫V div(F) dV
∫∫S F·dS = ∫V 0 dV
∫∫S F·dS = 0
Hence, the statement "Divergence theorem computes to zero for a solenoidal function" is true.
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