question_answer

Two small spheres each having the charge \[+Q\] are suspended by insulting threads of length L from a hook. This arrangement is taken is space where there is no gravitational effect, then the angle between the two threads and the tension in each will be:

A)  \[{{180}^{o}}\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{Q}^{2}}}{{{(2L)}^{2}}}\]    

B)  \[{{90}^{o}},\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{Q}^{2}}}{{{L}^{2}}}\]

C)  \[{{180}^{o}},\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{Q}^{2}}}{2{{L}^{2}}}\]      

D)  \[{{180}^{o}},\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{Q}^{2}}}{{{L}^{2}}}\]

Correct Answer: A

Solution :

The position of the balls in no gravity space will be as shown (The ball will attain a position at which angle between the threads would be \[{{180}^{o}}\])             As, \[\theta ={{180}^{o}},\] Than, force \[=\frac{1}{4\pi {{\varepsilon }_{0}}},\frac{{{Q}^{2}}}{{{(2L)}^{2}}}\]