Question
Download Solution PDF\(\vec r\) की दिशा में 1 / r का दिशात्मक अवकलज क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा :
माना कि f(r) एक फलन है तो फलन f(r) के दिशात्मक अवकलज को निम्न द्वारा दिया जाता है: \(\nabla f(r) = f'(r) \frac{\vec r}{|\vec r|}\)
गणना :
माना कि f(r) = 1/r
जैसा कि हम जानते हैं कि, यदि f(r) एक फलन है तो फलन f(r) के दिशात्मक अवकलज को निम्न द्वारा दिया जाता है: \(\nabla f(r) = f'(r) \frac{\vec r}{|\vec r|}\)
⇒ f'(r) = \(- \frac{1}{r^2}\)
यहाँ, \(r = |\vec r|\)
\(\nabla f(r) = - \frac{1}{r^2} \cdot \frac{\vec r}{r} = - \frac{\vec r}{r^3}\)
यहाँ, हमें \(\vec r\) की दिशा में f(r) के दिशात्मक अवकलज का पता लगाना होगा
\(\nabla f(r)\dot\ \frac{\vec r}{r}\ = - \frac{\vec r}{r^3}\ \dot\ \frac{\vec r}{r}\ = -\frac{\ r^2}{r^4}\ = - \frac{1}{r^2}\)
Last updated on Jul 17, 2025
-> RPSC 2nd Grade Senior Teacher Exam 2025 Notification has been released on 17th July 2025
-> 6500 vacancies for the post of RPSC Senior Teacher 2nd Grade has been announced.
-> RPSC 2nd Grade Senior Teacher Exam 2025 applications can be submitted online between 19th August and 17th September 2025
-> The Exam dates are yet to be announced.