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  • Given the field <img alt="E= (\frac{K}{r})\acute{a}" src="https://entrancecorner.oncodecogs.com/gif.latex?E%3

Given the field E= (\frac{K}{r})\acute{a}  in cylindrical coordinates then the work needed to move a point charge Q from any radial distance r to a point at twice that radial distance is-

 

Option: 1

-KQ ln2


Option: 2

-Kr ln 2


Option: 3

-2K ln Q


Option: 4

-KQ ln r


Answers (1)

best_answer

Since the field has only a radial component

dW =-QE⋅dl

=-QErdr       =   -KQ/r  dr

For the limits of integration use  r1 and   2r1

W= -KQ \int_{r_{1}}^{2r_{_{1}}} \frac{dr}{r}

W= -KQ ln_{r_{_{1}}}^{2r_{1}} = -KQ ln (2r_{1}- r_{1})

        = -KQ ln r_{1}

 

Posted by

Anam Khan

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