A 2.0-cm-diameter parallel-plate capacitor with a spacing of 0.50 mm is charged to 200 V. What are (a) the total energy stored in the electric field and (b) the energy density

Answer :

Answer:

(A) Total energy will be equal to [tex]0.044\times 10^{-5}J[/tex]

(b) Energy density will be equal to [tex]0.0175J/m^3[/tex]

Explanation:

We have given diameter of the plate d = 2 cm = 0.02 m

So area of the plate [tex]A=\pi r^2=3.14\times 0.02^2=0.001256m^2[/tex]

Distance between the plates d = 0.50 mm = [tex]0.50\times 10^{-3}m[/tex]

Permitivity of free space [tex]\epsilon _0=8.85\times 10^{-12}F/m[/tex]

Potential difference V =200 volt

Capacitance between the plate is equal to [tex]C=\frac{\epsilon _0A}{d}=\frac{8.85\times 10^{-12}\times 0.001256}{0.50\times 10^{-3}}=0.022\times 10^{-9}F[/tex]

(a) Total energy stored in the capacitor is equal to

[tex]E=\frac{1}{2}CV^2[/tex]

[tex]E=\frac{1}{2}\times 0.022\times 10^{-9}\times 200^2=0.044\times 10^{-5}J[/tex]

(b) Volume will be equal to [tex]V=Ad[/tex], here A is area and d is distance between plates

[tex]V=0.001256\times 0.02=2.512\times 10^{-5}m^3[/tex]

So energy density [tex]=\frac{Energy}{volume}=\frac{0.044\times 10^{-5}}{2.512\times 10^{-5}}=0.0175J/m^3[/tex]

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