The problem involves determining the radius of the outer sphere of a spherical condenser given its capacitance of 1uF and the spacing between the two spheres as 1mm. The relevant equation for capacitance in this context is provided.
The discussion is ongoing, with participants sharing their attempts at solving the equations and expressing their confusion regarding the quadratic equation that arises. Some guidance has been offered regarding the approach to take, but no consensus has been reached on the final solution.
Participants note the importance of showing all working steps in initial posts to facilitate better assistance. There is an acknowledgment of the complexity introduced by the quadratic equation derived from the initial equations.
You have two equations and two unknowns.James2911 said:Homework Statement
The capacitance of a spherical condenser is 1uF. If the spacing between the two spheres is 1mm, then what is the radius of the outer sphere
Homework Equations
[/B]
C = 4 pi Epsilon * ab/b-a (for a spherical capacitor)
The Attempt at a Solution
Given C = 1uF (u = 10^-6)
b-a = 10^-3
1uF = 4 pi Epsilon * ab/10^-3
On solving
9 = ab
How do I proceed forward from here? Please help
Yes I did but this is what happened;haruspex said:You have two equations and two unknowns.
Apply the standard method of solving simultaneous equations. Use one equation to express one variable in terms of the other, then substitute for it in the other equation.
Next time, please post your working as far as you get in the first post.James2911 said:Yes I did
It's just a quadratic equation. But it should be obvious what a will be approximately.James2911 said:a(a+10^-3) = 9
Still stuck! :(
I never saw that quadratic equation coming! Thank you. This it!haruspex said:Next time, please post your working as far as you get in the first post.
It's just a quadratic equation. But it should be obvious what a will be approximately.
By the way, I did not check your derivation of ab=9.