If \[\overrightarrow F \left( {\rho ,\,\phi ,\,z} \right) = \rho {{\hat a}_\rho } + \rho {\sin ^2}\phi {{\hat a}_\phi } - z{{\hat a}_z}\] which one of the following is TRUE?
A. \[\nabla .\overrightarrow F \left| {_{\phi = 0}} \right. < \nabla .\overrightarrow F \left| {_{\phi = \frac{\pi }{2}}} \right.\]
B. \[\nabla .\overrightarrow F \left| {_{\phi = \frac{\pi }{4}}} \right. = \nabla .\overrightarrow F \left| {_{\phi = 0}} \right.\]
C. \[\nabla .\overrightarrow F \left| {_{\phi = 0}} \right. > \nabla .\overrightarrow F \left| {_{\phi = \frac{\pi }{2}}} \right.\]
D. \[\nabla .\overrightarrow F \left| {_{\phi = \frac{\pi }{4}}} \right. = 2\nabla .\overrightarrow F \left| {_{\phi = 0}} \right.\]
Answer: Option D
This Question Belongs to Electronics And Communications Engineering >> Electromagnetic Field Theory
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