A capacitor consists of two 6.0-cm-diameter circular plates separated by 1.0 mm. The plates are...

veksetz

veksetz

Answered

2022-01-04

A capacitor consists of two 6.0-cm-diameter circular plates separated by 1.0 mm. The plates are charged to 150 V, then the battery is removed.
a. How much energy is stored in the capacitor?
b. How much work must be done to pull the plates apart to where the distance between them is 2.0 mm?

Answer & Explanation

ramirezhereva

ramirezhereva

Expert

2022-01-05Added 28 answers

We are given:
D=6cm, d=1mm, V=150V
a) The energy stored in the capacitor will be obtained using this formula:
U=12CV2
Where C is the capacitance of the capacitor and D is the potential
The capacitance we can get from the following formula:
C=ϵ0Ad
A capacitor consists of circular plates, so its surface is:
A=π×r2
And radius is:
r=D2=62=3cm
ϵ0 is the dialectric constznt of vacuum and has the following value:
ϵ0=8.854×1012Fm
Thus, the first formula becomes:
U=12×ϵ0πr2d×V2
Now, convert cm and mm into m
Finally, we have:
U=12×8.854×1012π×(3×102)21×103×(150)2
U=0.28×106J
b)Here the distance between the plates increases to d1=2mm
The work required to achieve will be obtained as the energy difference:
W=UU1
U1=12×8.854×1012π×(3×102)22×103×1502=0.14×106J
And we have:
W=0.28×1060.14×106
W=0.14×106J

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