Download App

Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance3 Marks
Question
A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (2.36). Show

that the capacitance of a spherical capacitor is given by $\text{C}=\frac{{4}\pi\in_{0}\text{r}_1\text{r}_2}{\text{r}_1-\text{r}_2}$

where r1 and r2 are the radii of outer and inner spheres, respectively.

✓

Answer

Radius of the outer shell = r1
Radius of the inner shell = r2
The inner surface of the outer shell has charge +Q.
$\text{V}=\frac{\text{Q}}{{4}\pi\in_0\text{r}_2}-\frac{Q}{{4}\pi\in_0\text{r}_1}$
The outer surface of the inner shell has induced charge −Q. Potential difference between the two shells is given by,
Where,
∈0 = Permittivity of free space
$\text{V}=\frac{\text{Q}}{{4}\pi\in_0}\bigg[\frac{1}{\text{r}_2}-\frac{1}{\text{r}_1}\bigg]$
$\text{V}=\frac{\text{Q}(\text{r}_1-\text{r}_2)}{{4}\pi\in_0\text{r}_1\text{r}_2}$
Capacitance of the given system is given by,
$\text{C}\frac{\text{charge}(\text{Q})}{\text{potential difference}(\text{V})}$
$=\frac{{4}\pi\in_0\text{r}_1\text{r}_2}{\text{r}_1-\text{r}_2}$
Hence, proved.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Electrostatic Potential and Capacitance→Electrostatic Potential and Capacitance — all question types→Physics STD 12 Science question papers→Bihar Board STD 12 Science question papers→Bihar Board question paper generator→

Similar questions

A light ray incident at grazing angle on the face AB of a prism ABC, follows the path shown in the figure. Obtain the relation between the angle of prism A and the refractive index $\mu$ of its material.

→
At what temperature the mean speed of the molecules of hydrogen gas equals the escape epeed from the earth?
→
Write the two processes that take place in the formation of a p-n junction. Explain with the help of a diagram, the formation of depletion region and barrier potential in a p-n junction.
→
In a p-n junction, the depletion region is 400nm wide and an electric field of 5 × 105V/m exists in it.
  1. Find the height of the potential barrier.
  2. What should be the minimum kinetic energy of a conduction electron which can diffuse from the n-side to the p-side?
→
Obtain the formula of electric current for an AC circuit having only capacitor.
→
  1. Write the important properties of photons which are used to establish Einstein’s photoelectric equation.
  2. Use this equation to explain the concept of (i) threshold frequency and, (ii) Stopping potential.
→
Define resolving power of a microscope. Write its formula. How will it be affected when
(i) the wavelength of incident light decreases and
(ii) the aperture of the objective decreases ?
→
A magnetic field of strength 1.0T is produced by a strong electromagnet in a cylindrical region of radius 4.0cm, as shown in the figure. A wire, carrying a current of 2.0A, is placed perpendicular to and intersecting the axis of the cylindrical region. Find the magnitude of the force acting on the wire.

→
If $\vec{\text{A}},\vec{\text{B}},\vec{\text{C}}$ are mutually perpendicular, show that $\vec{\text{C}}\times(\vec{\text{A}}\times\vec{\text{B}})=0.$ Is the converse true?
→
The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge –0.8 μC in air is 0.2 N.
  1. What is the distance between the two spheres?
  2. What is the force on the second sphere due to the first?
→