Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
The electric field E = dV/dr suggests that electric potential decreases along the direction of electric field.
Let us take any path from the charged conductor to the uncharged conductor along the direction of electric field. Therefore, the electric potential decrease along this path.
Now, another path from the uncharged conductor to infinity will again continually lower the potential further. This ensures that the uncharged body must be intermediate in potential between that of the charged body and that of infinity.
APPEARS IN
संबंधित प्रश्न
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 charge on the capacitor as shown in the circuit.
Find the ratio of energy stored in the two configurations if they are both connected to the same source.
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?
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.
Consider the situation shown in figure. The switch is closed at t = 0 when the capacitors are uncharged. Find the charge on the capacitor C1 as a function of time t.
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 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.
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 parallel plate capacitor has a uniform electric field ‘`vec "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)
In a capacitor of capacitance 20 µF, the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, what is the new capacitance?
A parallel combination of two capacitors of capacities ‘C’ and ‘`C/3`’ respectively is connected across a battery of 12 volt. When both capacitors are fully charged, the charge and energy stored in them is Q1, Q2 and E1, E2 respectively. Then the ratio of (E1 − E2) to (Q1 − Q2) is ______.
Which expression gives the work done in transferring charge \(q\) through potential difference \(V\) in a capacitor?
Which set gives the equivalent expressions for the energy stored in a capacitor?
What is the SI unit of energy stored in a capacitor?
A capacitor with capacitance \(3\times10^{-9}\,\mathrm{F}\) is connected to \(400\,\mathrm{V}\). A dielectric slab with \(K=3\) completely fills the space, and the voltage is kept constant. What is the energy change when the slab is removed?
