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1. Electric Charges and Fields
normal
Charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at distance $2\,L$ apart, $C$ is the midpoint between $A$ and $B$ . The work done in moving a charge $+ Q$ along the semicircle $CRD$ is
A
$ - \frac{{qQ}}{{6\pi \,{ \in _0}L}}$
B
$\frac{{qQ}}{{4\pi \,{ \in _0}L}}$
C
$\frac{{qQ}}{{2\pi \,{ \in _0}L}}$
D
$\frac{{qQ}}{{6\pi \,{ \in _0}L}}$
Solution
$\mathrm{W}=\Delta \mathrm{U}=\mathrm{Q}\left(\mathrm{V}_{\mathrm{D}}-\mathrm{V}_{\mathrm{C}}\right)$ here $\mathrm{V}_{\mathrm{C}}=0$
$ = Q\left[ {\frac{q}{{4\pi { \in _0}(3L)}} – \frac{q}{{4\pi { \in _0}(L)}} – 0} \right] = \frac{{ – Qq}}{{6\pi { \in _0}L}}$
Standard 12
Physics
