Two parallel plates of area 100 cm2 are given charges of equal magnitudes 8.9×10−7C but opposite signs. The electric field within the dielectric material filling the space between the plates is 1.4×106 V/m. (a) Calculate the dielectric constant of the material. (b) Determine the magnitude of the charge induced on each dielectric surface.
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(a) We apply Gauss’s law with dielectric and solve for k : κ=ε0EAq=(8.85×10−12C2/N.m2)(1.4×10−6V/m)(100×10−4m2)8..9×10−7C=7.2
(b) The charge induced is q′=q(1−κ1)=(8.9×10−7C)(1−7.21)=7.7×10−7C.
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