(b) Suppose that such a capacitor was made inthe form of a parallel-plate capaci

Question

(b) Suppose that such a capacitor was made inthe form of a parallel-plate capacitor with a vacuum between theplates and an electric field no greater than 3.00 x 106 V/m. What is theminimum area of the plates?

A capacitor is not the most efficient device for storing energy.Batteries can store more energy in much less space. For example, atypical 12 V automobile battery stores on the order of 1.00 x 106 J. (a) Find the capacitance necessary to store1.00 x 106 J with a potential difference of1.00 x 104 V across the capacitor'sterminals. (b) Suppose that such a capacitor was made inthe form of a parallel-plate capacitor with a vacuum between theplates and an electric field no greater than 3.00 x 106 V/m. What is theminimum area of the plates?

Explanation / Answer

Energy stored, U = 0.5C.V2                       C = 2U/V2 = 2x106/108 =0.02 F (b) E.d = V;           d = V/E= 104/3.0x106 = 0.00333m C = o.A/d      A = d.C/o.           =0.00333x0.02/8.85x10-12           =7.53x106m2

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