Sol::
Given ::
Q= 2.5*10^9
E= 1.6*10^5 N/C
We know that capacitance C is
C = ε*A/d
The charge on a capacitor is:
Q = C*V
= ( ε*A/d )*( E*d )
Q = ε*A*E
Where
A = π*r^2
= π*D^2/4
As
A= Q/( ε*E )
π*D^2/4= Q/( ε*E )
where "D" represents the plate diameter.
D^2 = 4*Q/( π*ε*E )
D = sqrt( 4*Q/( π*ε*E )
=sqrt[4*(2.5*10^9)*(1.6*10^-19) / ( π* (8.854*10^-12) * 1.6*10^5 )
]
D = 18.96*10^-3 m
≈ 19 mm
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