Chapter#1: Vector Analysis

Team Quanta presents all short questions of Methods of Mathematical Physics – I’s Chapter#1: Vector Analysis.

Q.1 Write the physical interpretation of Curl.

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Q.2 How vector field is solenoidal?

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Q.3 Verify the divergence theorem for cylinder $\mathbf{\vec{A}=x\hat{i}+y\hat{j}+z\hat{k}}$ . Also $\vec{\mathbf{\nabla}}\cdot\vec{\mathbf{A}}=\mathbf{3}$ .

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Q.4 Show that $\mathbf{\oint_{C}{\left(\vec{\nabla}\times\vec{r}\right)\vec{dl}=0}}$

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Q.5 Derive general form of Green’s Theorem.

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Q.6 Calculate the Green’s Value for the function F=Y²and G=x² for the region x=1 and y=2 form origin.

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Q.7 Find the divergence of vector $\vec{F}=x\ exp^{-x}\hat{i}+y\hat{j}-xz\hat{k}$

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Q.8 How to find the result of a vector?

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Q.9 Determine the divergence of $\vec{A}=30\hat{i}+2xy\hat{j}+5xz^2\hat{k}$ at (1,1,-0.2).

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Q.10 Write the laws of vector algebra.

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