The factor by which E is decreased and C is increased is defined to be the

# The factor by which e is decreased and c is increased

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The factor by which E is decreased and C is increased is defined to be the dielectric constant κ. 0 C C κ = κ / 0 E E =
Example: Problem 25-48 Given a parallel-plate capacitor, dielectric- filled, with area A = 100 cm 2 , charge Q = 890 nC, and electric field E = 1.4 kV/mm. (a) Find dielectric constant of the material. (b) Find the induced charge.
(a) ( ) 0 0 / / ε A q E = If there were no dielectric the field between the plates would be given by Gauss’s Law as m V E / 10 01 . 1 10 85 . 8 10 / 10 9 . 8 7 12 2 7 0 × = × × = 2 . 7 10 4 . 1 / 10 01 . 1 / 6 7 0 = × × = = E E So κ κ / 0 E E = But by definition:
0 / ε A q E Gauss tot = nC nC nC q q q so q q q But tot tot 766 124 890 ' ' = = = = nC C EA q So tot 124 10 4 . 12 10 10 4 . 1 10 85 . 8 8 2 6 12 0 = × = × × × × = = ε (b)

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