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Given the field $\vec{E}=\left(\frac{K}{r}\right) \hat{a}$ 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
$-kQ\ln\2$

Option: 2
$-kr\ln\2$

Option: 3
$-2k\ln\ Q$

Option: 4
$-kQ\ln\ r\bar{}$

Answers (1)

best_answer

Since the field has only a radial component
$\bar{dW}=-\bar{QE}.\bar{dE}$
$-QE_{r}dr=-\frac{kQ}{r}dr$
For the limits of integration use $r_{1}$ and   $2r_{1}$
   $W=-kQ\int_{r_{1}}^{2r_{1}} \frac{dr}{r}$
   $W=-kQ\left ( lnr \right )_{r_1}^{2r_1}$
$=-kQln\left ( 2r_{1}-r_{1} \right )$
   $=-kQlnr_{1}$

Posted by

Shailly goel

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