Electrostatics Question 113

Question: The mean electric energy density between the plates of a charged capacitor is (here $ q $ = charge on the capacitor and $ A $ = area of the capacitor plate) [MP PET 2002]

Options:

A) $ \frac{q^{2}}{2{\varepsilon _{0}}A^{2}} $

B) $ \frac{q}{2{\varepsilon _{0}}A^{2}} $

C) $ \frac{q^{2}}{2{\varepsilon _{0}}A} $

D) None of the above

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Answer:

Correct Answer: A

Solution:

Energy density $ =\frac{1}{2}{\varepsilon _{0}}E^{2}=\frac{1}{2}{\varepsilon _{0}}{{( \frac{\sigma }{{\varepsilon _{0}}} )}^{2}}=\frac{{{\sigma }^{2}}}{2{\varepsilon _{0}}}=\frac{q^{2}}{2{\varepsilon _{0}}A^{2}} $



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