A homemade capacitor is built by placing two flat steel cookie sheets next to ea

Question

A homemade capacitor is built by placing two flat steel cookie sheets next to each other, with thin rubber spacers in between, so that they are separated by 1.25 mm. One sheet is given a positive charge of 7.93 ?C, and the other is given an equal and opposite negative charge. Each sheet measures 35.0 cm by 45.0 cm. (a) What is the strength of the electric field between the sheets? (b) If extra spacers are inserted to double the separation between the sheets, what is the new electric field strength? (c) If the sheets are moved a kilometer apart, the electric field between them becomes essentially zero. Explain the discrepancy between this result and the results observed in parts "a" and "b" of this problem.

Explanation / Answer

(a)    magnitude of the charge on the one sheets , | Q |= | 7.93 C| = 7.93x10-6 C seperation between the plates , d = 1.25 mm = 1.25x10-3 m dimensions of the sheet =35.0 cm x 45.0 cm = 0.35 m x0.45 m thus, area of the sheet , A = (0.35 m) (0.45 m) = 0.1575 m2 but , It is known by the formula for capacitence of the parallel sheets Capacitence , C = Ao /d    ----(1) If potential difference b/w the sheets is V then , charge on the sheets , Q = CV ----(2) If E be the electric field existing b/w the sheets then , E = V / d    ---(3) plug , eqn(2) & (1) in (3) we have , E = Q /Cd = Q / [Ao /d]d = Q /Ao thus, electric field b/w the sheets ,                   E = Q / Ao    ------(4)
                          =( 7.93x10-6 C ) / ( 0.1575 m2  )(8.85x10-12 C2/Nm2)                         = ( 7.93x10-6 C ) / (1.393875x10-12)                         = 5.689 x106 N/C (b) & (c) If extra spacers are inserted to double the separation between the sheets, the new electric field strength is same as (a) , because from equation (4) it doesn't depends on the distance .thus, for part (c) also having the same value but , Actually field should be decreased as distance b/w the sheetes are increased hence ,a  discrepancy accur between this result and the results observed in parts "a" and "b" of this problem.

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