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The electrostatic force between the metal plates ofan isolated parallel plate capacitor C having acharge Q and area A, is :-
- a)independent of the distance between the plates.
- b)linearly proportional to the distance between theplates
- c)proportional to the square root of the distancebetween the plates.
- d)inversely proportional to the distance betweenthe plates.
Correct answer is option 'A'. Can you explain this answer?
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The electrostatic force between the metal plates ofan isolated paralle...
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Explanation:
To understand why the electrostatic force between the metal plates of an isolated parallel plate capacitor is independent of the distance between the plates, we need to consider the formula for the capacitance of a parallel plate capacitor.
The capacitance (C) of a parallel plate capacitor is given by the formula:
C = ε₀ * (A/d)
Where:
- C is the capacitance
- ε₀ is the permittivity of free space (a constant)
- A is the area of each plate
- d is the distance between the plates
Analysis:
Now, let's analyze the formula for capacitance and the relationship between the electrostatic force and the capacitance.
1. Capacitance (C) is directly proportional to the area of each plate (A).
- This means that increasing the area of the plates will increase the capacitance.
- Similarly, reducing the area of the plates will decrease the capacitance.
2. Capacitance (C) is inversely proportional to the distance between the plates (d).
- This means that increasing the distance between the plates will decrease the capacitance.
- Similarly, reducing the distance between the plates will increase the capacitance.
Implication:
Based on the analysis above, it can be concluded that the electrostatic force between the metal plates is independent of the distance between the plates.
This is because the electrostatic force (F) between the plates is given by the formula:
F = Q² / (2 * ε₀ * A)
Where:
- F is the electrostatic force
- Q is the charge on each plate
- ε₀ is the permittivity of free space (a constant)
- A is the area of each plate
As we can see, the electrostatic force is directly proportional to the charge on each plate (Q) and the area of each plate (A). The distance between the plates (d) does not appear in the formula for the electrostatic force.
Therefore, the electrostatic force between the metal plates of an isolated parallel plate capacitor is independent of the distance between the plates.
To understand why the electrostatic force between the metal plates of an isolated parallel plate capacitor is independent of the distance between the plates, we need to consider the formula for the capacitance of a parallel plate capacitor.
The capacitance (C) of a parallel plate capacitor is given by the formula:
C = ε₀ * (A/d)
Where:
- C is the capacitance
- ε₀ is the permittivity of free space (a constant)
- A is the area of each plate
- d is the distance between the plates
Analysis:
Now, let's analyze the formula for capacitance and the relationship between the electrostatic force and the capacitance.
1. Capacitance (C) is directly proportional to the area of each plate (A).
- This means that increasing the area of the plates will increase the capacitance.
- Similarly, reducing the area of the plates will decrease the capacitance.
2. Capacitance (C) is inversely proportional to the distance between the plates (d).
- This means that increasing the distance between the plates will decrease the capacitance.
- Similarly, reducing the distance between the plates will increase the capacitance.
Implication:
Based on the analysis above, it can be concluded that the electrostatic force between the metal plates is independent of the distance between the plates.
This is because the electrostatic force (F) between the plates is given by the formula:
F = Q² / (2 * ε₀ * A)
Where:
- F is the electrostatic force
- Q is the charge on each plate
- ε₀ is the permittivity of free space (a constant)
- A is the area of each plate
As we can see, the electrostatic force is directly proportional to the charge on each plate (Q) and the area of each plate (A). The distance between the plates (d) does not appear in the formula for the electrostatic force.
Therefore, the electrostatic force between the metal plates of an isolated parallel plate capacitor is independent of the distance between the plates.
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The electrostatic force between the metal plates ofan isolated parallel plate capacitor C having acharge Q and area A, is :-a)independent of the distance between the plates.b)linearly proportional to the distance between theplatesc)proportional to the square root of the distancebetween the plates.d)inversely proportional to the distance betweenthe plates.Correct answer is option 'A'. Can you explain this answer?
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