Solving for Charge Distribution on 2 Conducting Spheres & Rod

[bobmerhebi]

Homework Statement

2 conducting spheres with radii 2 & 3m are connected with a conducting rod of thickness 0.1m & length 0.5m. 500C charge is put on the 2m radius sphere.
Find the amount of charge on each sphere & on the rod.

Homework Equations

The Attempt at a Solution

By conservation of charges: Q₁ + Q₂ + Q₃ = 500 ... (1); Q₁ of rod & Q₂ & Q₃ of 2m & 3m radii spheres respectively.

As charges are uniformly distributed we have: \sigma₁ = \sigma₂ = \sigma₃

so Q₁/A₁ = Q₂/A₂ = Q₃/A₃ ... (2)



here i got stuck & don;t know how to continue. i know that i need to find 3 equations with 3 unkowns & solve the system, but I am not seeing these equation except for (1) & probably i have to use parts of (2).

could someone help please. thx

 

[fikus]

you have three equations, (1) and two equations in (2). Q_1/A_1 = Q_2/A_2 and Q_2/A_2 = Q_3/A_3.

 

[bobmerhebi]

thx 4 the help

 

[naresh]

As charges are uniformly distributed we have: \sigma₁ = \sigma₂ = \sigma₃

Can you justify this?

 

[bobmerhebi]

coz charges on conductors tend to uniformly distribute them selves. isn't it?