Air-Filled Capacitor A parallel-plate air-filledcapacitor having area 63 cm 2 an

Question

Air-Filled Capacitor A parallel-plate air-filledcapacitor having area 63 cm2and plate spacing 2.0 mm is charged to apotential difference of 450 V. (a) Find the capacitance.
1 pF
(b) Find the amount of excess charge on each plate.
2 nC
(c) Find the stored energy.
3 µJ
(d) Find the electric field between the plates.
4 V/m
(e) Find the energy density between the plates.
5 J/m3 (a) Find the capacitance.
1 pF
(b) Find the amount of excess charge on each plate.
2 nC
(c) Find the stored energy.
3 µJ
(d) Find the electric field between the plates.
4 V/m
(e) Find the energy density between the plates.
5 J/m3

Explanation / Answer

a ) Capacitance of a parallel plateCapacitor   C = 0 A /d                                                                      = 8.85*10-12 * 63 *10-4m2 /2.0*10-3 m                                                                      = 27.8 pF b ) charge on each plate Q = C V                                             = 27. 8*10-12 F * 450 V                                             = 12.5 n C c ) Energy stored is  U = 1/2 CV2                                     = 1 /2 * 27.8 pF * (450V)2                                     = 2.81J d )   Electric field between theplates   E =   V / d                                                               = 450 V / 2.0 *10-3 m                                                                =225 *103 V / m e ) Energy density uE  = 1 /2 0 E2                                   = 1 /2 *8.85*10-12 * ( 225 *103 V / m )2                                   = 0.2240 J / m3

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