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.
A 1uF spherical condenser is a type of capacitor that has a capacitance of 1 microfarad (uF). It consists of two conductive spherical plates separated by a dielectric material, such as air or a non-conductive material. When a voltage is applied to the plates, it stores electrical energy.
Finding the radius of the outer sphere is important because it determines the overall size and capacitance of the spherical condenser. It also affects the electric field strength and the amount of energy that can be stored in the condenser.
The radius of the outer sphere can be calculated using the formula r = √(C/4πε), where r is the radius in meters, C is the capacitance in farads, and ε is the permittivity of the dielectric material in farads per meter (F/m).
The permittivity value for air is approximately 8.854 x 10^-12 F/m. This value may vary slightly depending on factors such as temperature and pressure.
Yes, the radius of the outer sphere can be changed by altering the distance between the two conductive plates. However, the capacitance will also change accordingly, as it is directly proportional to the radius. The permittivity and the type of dielectric material used can also affect the radius of the outer sphere.