Advertisements
Advertisements
प्रश्न
A metal sphere of radius R is charged to a potential V.
- Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R.
- Show that the electrostatic field energy stored outside the sphere of radius 2 R equals that stored within it.
Advertisements
उत्तर
- potential of the inner metallic sphere is given by V = `1/(4pi∈_0) q/R`
capacitance of the capacitor formed by two concentric spheres of radii R and 2R is given by
`C = 4pi∈_0 (R xx 2R)/(2R-R)`
`C = 4pi∈_0 xx 2R`
potential of the outer sphere is given by
`V_2 = 1/(4pi∈_0) q/(2R) = V/2` - Electrostatic energy stored outside the sphere is given by `E = 1/2C(V - V_2)^2`
`E = 1/2 xx 4pi∈_0 xx 2R xx V^2/4`
`E = pi∈_0 xx RV^2`
APPEARS IN
संबंधित प्रश्न
Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.
A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor?
Find the charge on the capacitor as shown in the circuit.
A capacitance C, a resistance R and an emf ε are connected in series at t = 0. What is the maximum value of (a) the potential difference across the resistor (b) the current in the circuit (c) the potential difference across the capacitor (d) the energy stored in the capacitor (e) the power delivered by the battery and (f) the power converted into heat?
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.
A 100 μF capacitor is joined to a 24 V battery through a 1.0 MΩ resistor. Plot qualitative graphs (a) between current and time for the first 10 minutes and (b) between charge and time for the same period.
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.
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?
How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?
A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating ∫ i2R dt and also by finding the decrease in the energy stored in the capacitor.
By evaluating ∫i2Rdt, show that when a capacitor is charged by connecting it to a battery through a resistor, the energy dissipated as heat equals the energy stored in the capacitor.
Obtain the expression for the energy stored in a capacitor connected across a dc battery.
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 ______.
A 2µF capacitor is charge to 100 volt and then its plate are connected by a conducting wire. The heat produced is:-
What fraction of the energy drawn from the charging battery is stored in a capacitor?
A 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 ______
(ε0 = permittivity of free space)
Do free electrons travel to region of higher potential or lower potential?
Prove that, if an insulated, uncharged conductor is placed near a charged conductor and no other conductors are present, the uncharged body must be intermediate in potential between that of the charged body and that of infinity.
Derive an expression for energy stored in a capacitor.
