Four identical charge particles of charge -1 C and mass 100g each are attached to four insulated identical and ideal strings whose other ends are attached to a single point with a ceiling. In equilibrium condition under graviyt what will be the tension in each string and also find the minimum and the maximum distance between any two charge particles in the given arrangement....

 

PS: I want the full solution, and the answer too....

HI Mansi, Lets see how we can approach for such a problem. The symetry of the problem suggests that the four charges will form a square (let say of side a). For general solution lets take length of string to be l, mass and charge of a signgle charge as m & q.

 

Electric force (F_e) on any given charge because of other three

= kq^2/(2a^2)               -------(from charge digonally opposite)

+2*kq^2*sin(45^o)/(a^2) -------- (from two adjecent charges. sin(45) comes as only component in digonal direction will add up)

 

Gravitational force on mass=(F_g)=mg

Resultant of both is balanced by tension which acts along the string. Let this string makes an angle theta with vertical. Then

sin(theta)=(a/root(2))/l = F_e/root(F_e²+F_g²)

 

Solve t his to get a.

Minimum distance between charges =a

Maximum distance = root(2)*a