Question

Find the capacitance of a spherical capacitor whose electrodes have radii R¹and R² where R² is greater which is filled with isotropic dielectric whose permittivity varies as k=a/r, where a is a constant, and r is the distance from the centre of the capacitor.​

Answer 1

Answer:

1 cm = 10 mm

100 cm = 1 m

1000 m = 1 km

100 m = 0.5 km

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Explanation:

Answer 2

$\huge\mathtt\pink{A}\mathtt\red{N}\mathtt\blue{S}\mathtt\green{W}\mathtt\purple{E}\mathtt\green{R}$

$\huge \: c = \frac{4\pi \epsilon_o a}{ ln( \frac{r2}{r1} ) }$

Explanation:

formula for potential difference=

$\huge\varDelta \: v = \int_{r_1}^{r_2}E. \delta r$

$\huge\varDelta \: v = \int_{r_1}^{r_2} \frac{kq}{ {r}^{2} \times \: K } \delta r$

$\huge\varDelta \: v = \int_{r_1}^{r_2} \frac{kqr}{ {r}^{2} \times \: a } \delta r$

$\huge\varDelta \: v = \frac{kq}{a} \int_{r_1}^{r_2} \frac{1}{r } \delta r$

$\huge\varDelta \: v = \frac{kq}{a} \int_{r_1}^{r_2} | ln(r) |$

$\huge \: \varDelta \: v = \frac{kq}{a} ln( \frac{r2}{r1} )$

Now C=q/v

Now put values

$\huge \: c= \frac{q}{ \frac{kq}{a} ln( \frac{r2}{r1} ) }$

$\huge \: c = \frac{4\pi \epsilon_o a}{ ln( \frac{r2}{r1} ) }$

Additional information

• Another formula for potential is
• C=$\huge\frac{\epsilon_0 A}{d}$
• If dielectric is given than electric field become E/k where k is dielectric constant