A) \[3F\]
B) \[\frac{F}{9}\]
C) \[F\]
D) \[\frac{F}{3}\]
Correct Answer: D
Solution :
: Let us call spheres as A and B. According to Coulomb s law, the force of repulsion between A and B separated by a distance d is \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{(+6\mu C)(+9\mu C)}{{{d}^{2}}}\] ??(i) When a charge of \[-3\mu C\] is given to both the spheres, then charge on \[A=+6\mu C-3\mu C\] \[=+3\mu C\] and on s\[B=+9\mu C-3\mu C=+6\mu C\] Again by Coulombs law, the new force of repulsion between A and B separated by the same distance d is \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{(+3\mu C)(+6\mu C)}{{{d}^{2}}}\] Dividing eqn. (ii) by eqn. (i), we get \[\frac{F}{F}=\frac{\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{(+6\mu C)(+9\mu C)}{{{d}^{2}}}}{\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{(+6\mu C)(+9\mu C)}{{{d}^{2}}}}\] \[=\frac{(+3\mu C)(+6\mu C)}{(+6\mu C)(+9\mu C)}=\frac{1}{3}\] or \[F=\frac{F}{3}\]You need to login to perform this action.
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