Question

Two parallel-plate capacitors, identical except that one has twice the plate separation of the other, are charged by the same voltage source. Which capacitor has a stronger electric field between the plates

Answer 1

Answer:

The capacitor having less distance of separation has a stronger electric field.

Explanation:

The capacitors are identical and only difference between them is that one has twice the plate separation of the other. Therefore, capacitance of the given capacitors C1 and C2 is,

C1= Aε/d  and C2=Aε/2d

The charges Q1 and Q2 on the capacitors of capacitance C1 and C2 respectively, is then given by the equation,

Q1=VC1

Q1=VAε/d

Q2=VC2

Q2=VAε/2d

Therefore, the surface charge density σ1 and σ2 for the capacitors is,

σ1=Q1/A

σ1=VAε/(d*A)

σ1=Vε/d

Similarly,

σ2=Q2/A

σ2=Vε/2d

The electric field between the plates is directly proportional to the surface charge density. And so electric field is inversely proportional to the distance of separation. Therefore the capacitor whose distance of separation is less has a stronger electric field.

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