Work done in moving the plates of the capacitors

In summary, the work done in moving a circular parallel plate capacitor with radius r>>d, initially charged to potential V, from separation d to d1 is AεV^2(d1/d-1)/2d. This can also be calculated using U=Q^2/2C, where Q is the charge which does not change when the capacitor is disconnected. Both methods yield the same result.
  • #1
bs vasanth
16
1
A parallel plate capacitor of circular cross section r>>d, and separation d. It is charged to potential V then disconnected from the circuit . What will be the work done in moving the capacitor from d to d1?

Answer:
Here the initial energy is 1/2C[itex]V^{2}[/itex]
Where C=Aε/d
While moving the capacitor both the capacitance and potential change:
Cf= Aε/d1
Vf=∫E.dl (with the limits 0 to d1)
Vf= E*d1
We know that the E doesn't change ( Under the approx. as r>>d )
Therefore initial potential and final potential can be related as V= E*d
Vf=V*d1/d
Work done = 1/2( Cf*[itex]Vf^{2}[/itex] - C*[itex]V^{2}[/itex] )
= Aε/2 ([itex](V*d1/d)^{2}/d1[/itex] - C*[itex]V^{2}/d[/itex] )
= [itex]AεV^{2}( d1/d -1)/2d[/itex]
I want to know if this answer is correct.
 
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  • #2
It's easier to use U=Q^2/2c because Q doesn't change for a disconnected capacitor, but your answer is correct.
 
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Related to Work done in moving the plates of the capacitors

1. How is work done in moving the plates of the capacitors?

The work done in moving the plates of the capacitors is a measure of the energy required to move the plates from one position to another. This energy is stored in the form of electric potential energy in the capacitor.

2. What factors affect the amount of work done in moving the plates of the capacitors?

The amount of work done in moving the plates of the capacitors is affected by the distance between the plates, the magnitude of the charge on the plates, and the strength of the electric field between the plates.

3. How is the work done calculated for moving the plates of the capacitors?

The work done can be calculated by multiplying the magnitude of the charge on the plates by the potential difference between the plates. This can be written as W = qΔV, where q is the charge and ΔV is the potential difference.

4. Is the work done in moving the plates of the capacitors always positive?

No, the work done in moving the plates of the capacitors can be either positive or negative. If the plates are moved in the same direction as the electric field, the work done is positive. If the plates are moved in the opposite direction of the electric field, the work done is negative.

5. How does the work done in moving the plates of the capacitors relate to the capacitance of the capacitor?

The work done is directly proportional to the capacitance of the capacitor. This means that a higher capacitance will require more work to move the plates compared to a lower capacitance.

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