Question:
A scalar potential \(\Psi\) has the gradient defined as \(\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}\). The value of the integral \(\int_c\nabla\Psi.d\overrightarrow{r}\) on the curve \(\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}\), where curve C: x=t, y = t2, z = 3t2 (1 ≤ t ≤ 3) is:
A scalar potential \(\Psi\) has the gradient defined as \(\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}\). The value of the integral \(\int_c\nabla\Psi.d\overrightarrow{r}\) on the curve \(\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}\), where curve C: x=t, y = t2, z = 3t2 (1 ≤ t ≤ 3) is:
Updated On: Mar 12, 2025
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The Correct Option is D
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The correct answer is(D): 726
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