Question
Obtain the curl of the following vector field: A = (eˆ r + r cos θeˆ θ + r eφ)
Answer :
Word Count : 385
______ ______ ______ ________ _____ __________ ________.
____ _______ __________ ________ __________ ______ _______ __________ _____ __________ _________.
______ ____ ___ _________ ___ __________ ______ ___ __________ ______.
__________ __________ __________ ____ _________ ________ ________.
______ ______ ________ _____ _______ ________ ___ ____ ____.
___ ___ ____ _________ ___ _____ __________ __________.
_______ _____ ____ _________ ______ _____ _______ _____ ___.
__________ _________ _______ ________ ___ ___ __________ ________ __________ __________.
___ ___ ________ __________ ________ ________ ___ ________.
______ ______ ____ _____ _____ _________ ____ _________ ____ ________ _______.
_______ _________ __________ ____ _____.
______ _____ __________ ______ __________ ____ ___ ______ __________ ________ ____ __________.
_________ ______ ____ ______ _________ ______ _______.
_______ ____ ________ _______ ___ __________ _____ ________.
_________ _________ __________ _____ ________ ________ _________ _____ ____ ________ _____.
_________ ________ __________ ________ ____ _______ ______ __________ ____ _______.
_______ ____ _____ ________ _________ _________ _____ ___ ___ _____.
____ ________ _______ ________ __________ _________ _____ _______.
_____ __________ _______ _______ __________ ________ _________ ________ ________ _________ __________ ______.
________ ______ _________ __________ __________ ______ _________ ___ _______ __________ ____ ______.
_______ ____ ______ _______ ______ _____ ______ ____ ________ ___.
_____ ____ _______ _____ ____ _________ _______.
____ _______ __________ _________ _____ ___ _________ __________ __________ _____.
______ ______ _________ __________ _______ ______ _________ ___ _________ ____.
____ ________ ________ ________ _____.
__________ ____ _____ ________ ___.
Skip in 10
To compute the curl of the given vector field \(\mathbf{A} = r \hat{e}_r + r \cos(\theta) \hat{e}_\theta + r \hat{e}_\phi\), we need to express it in cylindrical coordinates \((r, \theta, \phi)\) and apply the curl operator in these coordinates. ### Step 1: Curl in Cylindrical Coordinates The formula for the curl of a vector field \(\mathbf{A} = A_r \hat{e}_r + A_\theta \hat{e}_\theta + A_\phi \hat{e}_\phi\) in cylindrical coordinates is: \[ \nabla \times \mathbf{A} = \left( \frac{1}{r} \left( \frac{\partial A_\phi}{\partial \theta} - \frac{\partial A_\theta}{\partial \phi} \right) \right) \hat{e}_r + \left( \frac{1}{r} \left( \frac{\partial A_r}{\partial \phi} - \frac{\partial A_\phi}{\partial r} \right) \right) \hat{e}_\theta + \left( \frac{1}{r} \left( \frac{\partial A_\theta}{\partial r} - \frac{\partial A_r}{\partial \theta} \right) \right) \hat{e}_\phi \] ### Step 2: Components of \(\mathbf{A}\) We have the vector field: \[ \mathbf{A} = r \hat{e}_r + r \cos(\theta) \hat{e}_\theta + r \hat{e}_\phi \] From this,
____ _________ _________ ________ _________ ________ ________ ___ ____ _______ _________.______ ______ ______ ________ _____ __________ ________.
____ _______ __________ ________ __________ ______ _______ __________ _____ __________ _________.
______ ____ ___ _________ ___ __________ ______ ___ __________ ______.
__________ __________ __________ ____ _________ ________ ________.
______ ______ ________ _____ _______ ________ ___ ____ ____.
___ ___ ____ _________ ___ _____ __________ __________.
_______ _____ ____ _________ ______ _____ _______ _____ ___.
__________ _________ _______ ________ ___ ___ __________ ________ __________ __________.
___ ___ ________ __________ ________ ________ ___ ________.
______ ______ ____ _____ _____ _________ ____ _________ ____ ________ _______.
_______ _________ __________ ____ _____.
______ _____ __________ ______ __________ ____ ___ ______ __________ ________ ____ __________.
_________ ______ ____ ______ _________ ______ _______.
_______ ____ ________ _______ ___ __________ _____ ________.
_________ _________ __________ _____ ________ ________ _________ _____ ____ ________ _____.
_________ ________ __________ ________ ____ _______ ______ __________ ____ _______.
_______ ____ _____ ________ _________ _________ _____ ___ ___ _____.
____ ________ _______ ________ __________ _________ _____ _______.
_____ __________ _______ _______ __________ ________ _________ ________ ________ _________ __________ ______.
________ ______ _________ __________ __________ ______ _________ ___ _______ __________ ____ ______.
_______ ____ ______ _______ ______ _____ ______ ____ ________ ___.
_____ ____ _______ _____ ____ _________ _______.
____ _______ __________ _________ _____ ___ _________ __________ __________ _____.
______ ______ _________ __________ _______ ______ _________ ___ _________ ____.
____ ________ ________ ________ _____.
__________ ____ _____ ________ ___.
IGNOU ACADEMY
Your IGNOU journey, made easier.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
Continue Reading — It's Free
Sign in with Google to unlock more of this answer.
✓ Free access
✓ Unlock up to 60% of the answer
✓ No payment required
✓ Unlock up to 60% of the answer
✓ No payment required
Quick Google sign-in. No separate registration form.