हिंदी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान कक्षा ११

A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin. - Physics

Advertisements
Advertisements

प्रश्न

A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.

संख्यात्मक
Advertisements

उत्तर

Given :
Charge on the sphere = Q

Radius of the sphere = R

Capacitance of the sphere, C = 4πε0R

Thus, the energy of the sphere is given by 

`E = 1/2 CV^2`

= `1/2 xx 4pi∈_0RC = Q_2/(4pi∈_0R)^2`

= `Q^2/(8pi∈_0R)`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Capacitors - Exercises [पृष्ठ १६८]

APPEARS IN

एचसी वर्मा Concepts of Physics Vol. 2 [English] Class 11 and 12
अध्याय 9 Capacitors
Exercises | Q 41 | पृष्ठ १६८

संबंधित प्रश्न

Explain what would happen if the capacitor given in previous question a 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates,

  1. While the voltage supply remained connected.
  2. After the supply was disconnected.

A capacitor C1 of capacitance 1 μF and a capacitor C2 of capacitance 2 μF are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at t = 0.

(a) The current in each of the two discharging circuits is zero at t = 0.

(b) The currents in  the two discharging circuits at t = 0 are equal but not zero.

(c) The currents in the two discharging circuits at t = 0 are unequal.

(d) C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge.


Find the charge on the capacitor shown in the figure.


(a) Find the current in the 20 Ω resistor shown in the figure. (b) If a capacitor of capacitance 4 μF is joined between the points A and B, what would be the electrostatic energy stored in it in steady state?


A 20 μF capacitor is joined to a battery of emf 6.0 V through a resistance of 100 Ω. Find the charge on the capacitor 2.0 ms after the connections are made.


How many time constants will elapse before the charge on a capacitors falls to 0.1% of its maximum value in a discharging RC circuit?


A capacitor with stored energy 4⋅0 J is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors.


A capacitor of capacitance 100 μF is connected across a battery of emf 6 V through a resistance of 20 kΩ for 4 s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4 s after the battery is disconnected?


A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.


A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an ideal battery of emf ε through a resistance R. Find the charge on the capacitor at time t.


A metal sphere of radius R is charged to a potential V.

  1. Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R.
  2. Show that the electrostatic field energy stored outside the sphere of radius 2 R equals that stored within it.

Figure shows two identical parallel plate capacitors connected to a battery through a switch S. Initially, the switch is closed so that the capacitors are completely charged. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. Find the ratio of the initial total energy stored in the capacitors to the final total energy stored.


Choose the correct option:

Energy stored in a capacitor and dissipated during charging a capacitor bear a ratio.


A capacitor is a device that stores ____________.


If the p. d. across a capacitor is increased from 10 V to 30 V, then the energy stored with the capacitor ____________.


A 2µF capacitor is charge to 100 volt and then its plate are connected by a conducting wire. The heat produced is:-


Do free electrons travel to region of higher potential or lower potential?


A fully charged capacitor C with initial charge q0​ is connected to a coil of self-inductance L at t = 0. The time at which the energy is stored equally between the electric and magnetic fields is ______.


Derive an expression for energy stored in a capacitor.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×