Advertisements
Advertisements
Question
A large conducting plane has a surface charge density `1.0 xx 10^-4 "Cm"^-2` . Find the electrostatic energy stored in a cubical volume of edge 1⋅0 cm in front of the plane.
Advertisements
Solution
Given,
Surface charge density of the plane, `σ = 1.0 xx 10^-4 C/m^2`
Volume of the cube, `V = a^3 = 10^-6 "m"^3`
Electric field near the charged conducting plane is given as , `E = σ/∈_0` .... (i)
Energy density of electric filed,
`u = 1/2∈_0E^2`
⇒ `u = 1/2∈_0(σ/∈_0)^2`
⇒ `u = 1/2 σ^2/∈_0`
⇒ `u = 1/2 xx (1.0 xx 10^-4)^2/(8.85 xx 10^-12)`
⇒ `u = 0.056 xx 10^4 j/m^3`
`Volume = 10^-6 "m"^3`
⇒ `U = u xx V`
⇒ `U = 0.056 xx 10^4 xx 10^-6`
⇒ `U = 5.6 xx 10^-4 J`
APPEARS IN
RELATED QUESTIONS
A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor?
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
Find the ratio of energy stored in the two configurations if they are both connected to the same source.
Find the charge on the capacitor shown in the figure.
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.
The plates of a capacitor of capacitance 10 μF, charged to 60 μC, are joined together by a wire of resistance 10 Ω at t = 0. Find the charge on the capacitor in the circuit at (a) t = 0 (b) t = 30 μs (c) t = 120 μs and (d) t = 1.0 ms.
How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.
Each capacitor in figure has a capacitance of 10 µF. The emf of the battery is 100 V. Find the energy stored in each of the four 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.
Choose the correct option:
Energy stored in a capacitor and dissipated during charging a capacitor bear a ratio.
If the p. d. across a capacitor is increased from 10 V to 30 V, then the energy stored with the capacitor ____________.
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is ______.
A capacitor is charged by a battery and energy stored is 'U'. Now the battery is removed and the distance between plates is increased to four times. The energy stored becomes ______.
An air-filled parallel plate capacitor has a uniform electric field `overset(->)("E")` in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is ______
(∈0 = permittivity of free space)
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.
