The plates of a parallel plate capacitor have an area of 90cm2 each and are separated by 2.5mm. The capacitance is charged by connecting it to a 400V supply.
(a) How much electrostatic energy is stored by the capacitor ?
(b) View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume (u). Hence arrive at a relation between U and the magnitude of electric field E between the plates.
Area of the plate of a parallel plate capacitor, A=90cm2=90×10−4m2
Distnace betweent he plates , d=2.5 mm =2.5×10−3m
potential difference across the plates , V=400 v
(a) capacitance of the capacitor is given by the relation.
C=∈0Ad
Electrostatic energy stored in the capacitor is given by the relation , E1=12CV2
=12∈0AdV2
where, ∈0=permitivity of free space =8.85×10−12C2N−1m−2
∴E1=1×8.85×10−12×90×(400)22×2.5×10−3=2.55×10−6J
Hence, the electrostatic energy stored by the capacitor is 2.55×10−6J
(B) volume of the given capacitor
V'=A×d
=90×10−4×25×10−3
=2.25×10−4m3
Energy stored in the capacitor per unit volume is given by
u=E1V'
=2.55×10−62.25×10−4=0.11Jm−3
Again u=E1v'
=12CV2Ad=∈0A2dV2Ad=12∈0(Vd)2
where,
Vd=electric intensity =E
∴u=12∈0E2
Related Playlists
- BOOK - NCERTCHAPTER - ELECTROSTATIC POTENTIAL AND CAPACITANCEEXERCISE - Exercise37videos
ELECTROSTATIC POTENTIAL AND CAPACITANCE
- BOOK - NCERTCHAPTER - ELECTROMAGNETIC WAVESEXERCISE - Exercise15videos
ELECTROMAGNETIC WAVES
- BOOK - NCERTCHAPTER - MAGNETISM AND MATTEREXERCISE - Exercise25videos
MAGNETISM AND MATTER
Similar Questions
The plates of a parallel plate capacitor have an area of 90cm2? each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply.
How much electrostatic energy is stored by the capacitor ?View SolutionThe plates of a parallel plate capacitor have an area of 90cm2 each and are separated by a 2mm The capacitor is charged by connecting it to a 400V supply.Then the density of the energy stored in the capacitor ..........?
View SolutionThe plates of a parallel plate capacitor have an area of 90cm2? each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply.
View this energy as stored in the electrostatic field between the plates and obtain the energy per unit volume u. Hence arrive at a relation between u and the magnitude of electric field E between the plates.View SolutionThe plates of a parallel plate capacitor have an area of 100cm2 each and area separated by 2.5 mm. the capacitor is charged to 200V. Calculate the energy stored in the capacitor.
View SolutionThe plates of a parallel plate capacitor have an area of 90cm2 and each are separated by 2mm. The capacitor is charged by connecting it to a 400 V supply. Then the energy density of the energy stored (in Jm−3) in the capacitor is (take ε0=8.8×10−12Fm−1)
View SolutionA 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor ?
View SolutionA 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor ?
View SolutionThe plates of a parallel plate capacitor have on area of 90cm2 each and are separated by 2.5mm. The capacitor is charged to 400 V. How much electrostatic energy is stored in it ? How much when it is filled with a dielectric medium K=3 and then charged ? If it is first charged as an air capacitor and then filled with th dielectric, then ?
View SolutionCalculate capacitance of a parallel plate capacitor with area of each plate 1 cm2 and separation 1 mm.
View SolutionA capacitor of capacitance 700 pF is charged by 100 V battery. The electrostatic energy stored by the capacitor is
View Solution