If [overrightarrow F ( , ,z ) = hat a_ + sin ^2 hat a_ - zhat a_z] which one of the following is TRUE?

[ .overrightarrow F | _ = 4 . = 2 .overrightarrow F | _ = 0 .]

This question belongs to Electronics And Communications Engineering Electromagnetic Field Theory

Electromagnetic Field Theory

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 & Solution

Correct Answer: Option D

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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?

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