Express \(\vec{B} = \frac{10}{r}\hat{r} + r\cos\theta\hat{\theta} + \hat{\phi}\) in cartesian and cylindrical co-ordinate at (-3, 4, 0) and (5, \frac{\pi}{2}, -2).
Solution
\(\vec{B} = -2\hat{x} + \hat{y}\)
\(\vec{B} = 2.5\hat{r} + \hat{\phi} + 1.167\hat{z}\)