Question

निम्नलिखित सदिश क्षेत्र का डाइवर्जेन्स और कर्ल प्राप्त करेंः

equation

23 Jan 2025
Answer :
Word Count : 402
दिया गया सदिश क्षेत्र \(\vec{A}\) है: \[ \vec{A} = (\rho z \hat{e}_{\rho} + \rho^2 \hat{e}_{\phi} + \rho z \sin\phi \hat{e}_{z}) \] अब हमें इसका डाइवर्जेन्स और कर्ल निकालने हैं। ### 1. डाइवर्जेन्स (\(\nabla \cdot \vec{A}\)): डाइवर्जेन्स का सूत्र इस प्रकार होता है: \[ \nabla \cdot \vec{A} = \frac{1}{\rho} \frac{\partial}{\partial \rho} (\rho A_{\rho}) + \frac{1}{\rho} \frac{\partial}{\partial \phi} A_{\phi} + \frac{\partial}{\partial z} A_{z} \] यहाँ \(\vec{A}\) के घटक हैं: ________ _____ ____ _____ ___.
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