(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the capacitance of a spherical capacitor such that its center and up to [tex]R_2[/tex] is vacuum.

Then from [tex]R_2[/tex] up to [tex]R_3[/tex] there's a dielectric material of constant [tex]\kappa _2[/tex]. Then from [tex]R_3[/tex] up to [tex]R_1[/tex] there's a material of constant [tex]\kappa _1[/tex].

2. Relevant equations

None given.

3. The attempt at a solution

I've tried many things, but then I realized I was lost since it's a 3 dimensional capacitor, which differs from the 2 dimensional problem I was used to.

Q=C/V. Also, [tex]\varepsilon _1=\kappa _1 \varepsilon _0[/tex]. And it's similar for [tex]\varepsilon _2[/tex].

[tex]V=-\int_a^b \vec E d\vec l=\frac{Q}{C}[/tex].

I'm having a hard time finding [tex]-\int_a^b \vec E d\vec l[/tex].

For the interior material, [tex]V=E(R_3 -R_2)[/tex].

I made an attempt to find E : [tex]kQ\left [ \frac{1}{R_3}-\frac{1}{R_2} \right][/tex]. Where [tex]k=\frac{1}{\varepsilon _0 \kappa _2 4\pi}[/tex].

Hence [tex]C _2=\frac{4\pi \varepsilon _0 \kappa _2 R_3 R_2}{R_2-R_3}[/tex].

I realize that [tex]\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}[/tex] because the capacitor is equivalent to 2 capacitors in series. I'd like to know if my result for [tex]C_2[/tex], the interior capacitor is right.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Calculate the capacitance

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