Q1 Three identical charged small spheres each of mass m are suspended from a common point by insulated light string each of length l.The spheres are always on vertices of equilateral triangle of side length x<<<l .Calculate the rate dq/dt with which charge on each sphere increase if length of the sides of triangle increases according to law dx/dt = a/ x

Q2 Two mutually perpendicular long straight conductors carrying  uniformly distributed charges of linear charge densities _`1 and ₂ are positioned at distance a from each other.How does the interaction between the rods depend on a?

PLZZ help!!!!!!

Q2 independant of a

for wire 2

let x be distance of a piece of thickness dx from the point where they are perpendicular.

Then E1(x) = (lambda1)/2pi*epsilon*root(a^2+x^2)

then force on dx = (lambda1*lambda2*dx)/2pi*epsilon*root(a^2+x^2)

now horizontal component cancel and vertical remain

so dF(x) = (lambda1*lambda2*dx*a)/2pi*epsilon*(a^2+x^2)

evaluate integral from 0 to infinity it comes independant of a

q1 . Draw the FBD of any of the charged ball

Assume that the string connected to it makes an angle  with the vertical .

Then we have T cos = mg

                           T sin = q^2/x^2 sqrt ( 3 ) ( resultant of two forces )

so , tan  = q^ 2sqrt ( 3 ) / x^2 mg = x / sqrt(3 ) l ( from geqmetry with approximation )

  solving for q , we get q = k x^(3/2)

or dq/dt = 3/2k sqrt ( x )dx/dt = c ( since dx/dt = a/ sqrt(x ) )

 so , q = ct , c being a constant ( determine it by putting the value of k )

The calculation is done in CGS units .

feymann cant understand your solution

Plus your answer is also wrong

Plzzzzz try again and explain clearly.........

Give the answer .

The method is clear enough . 

But put clearly the value of dx/dt  . Can't read properly .

I have taken that to be a/sqrt(x ) . In that case , the answer is pretty correct !!

The answer ( more precisely the value of c) would be different (  a factor of 4pi epsilon naught would be present ) if the calculation is done in SI method .But in that case also q must be proportioal to time .

Also the qn is incomplete !! It has not mentioned what initial charge was present in the balls . I have taken that to be zero .

Are u having problem with the value of c ? Let me know !

waiting for an answer !!!

exactly ! ( I have not put the value of constant c , left as a problem (: )

See , u also get dq/dt = constant , just like me .

OK OK feynmann gr888888 job

thanxxxxxxxx