Two parallel plates are 0.005 m apart and are each2m 2 in area. The plates are i

Question

Two parallel plates are 0.005 m apart and are each2m2 in area. The plates are in vacuum and an electricpotential difference of 10,000 V is applied across them. (a) Find capacitance, the charge on each plate, the electricfield intensity in the space between the plates, and the storedenergy. (b) If a dielectric material with deielectric constant k=80.4is inserted into the gap between the plates, with the electricpotential remaining the same, find the new capacitance, charge oneach plate, electric field intensity, and energy stored. Thanks in advance for any help! Two parallel plates are 0.005 m apart and are each2m2 in area. The plates are in vacuum and an electricpotential difference of 10,000 V is applied across them. (a) Find capacitance, the charge on each plate, the electricfield intensity in the space between the plates, and the storedenergy. (b) If a dielectric material with deielectric constant k=80.4is inserted into the gap between the plates, with the electricpotential remaining the same, find the new capacitance, charge oneach plate, electric field intensity, and energy stored. Thanks in advance for any help!

Explanation / Answer

a ) The capacitance of the capacitor is               C = o A / d = 8.85 x 10-12 *2 / 0.005 = 3.540 x 10-9 F         Charge on the plates               Q = C V = 3.540 x 10-9 * 10000 = 3.540 x 10-5C         Electric field betweenthe plates              E = V d = 10000 * 0.005 = 50 N / C         Energy stored in thecapacitor              U = 0.5 CV2 = 0.5 * 3.540 x 10-9 *108 = 0.1770 J b)          The capacitance ofthe capacitor is               C = ko A / d = 80.4 * 8.85 x10-12 * 2 / 0.005 = 284.616 x10-9 F         Charge on the plates               Q = C V = 284.616 x 10-9 * 10000 = 284.616 x10-5 C         Electric field betweenthe plates              E = V d = 10000 * 0.005 = 50 N / C         Energy stored in thecapacitor              U = 0.5 CV2 = 0.5 * 284.616 x 10-9 *108 = 14.23 J

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