a) What is the electric field in the region just above the center of the top pla

Question

a) What is the electric field in the region just above the center of the top plate; i.e. on the "outside"?

b) What is the electric field between the plates near the center of the plates?

c) What is the potential difference between the plates?

d) What is the capacitance of the configuration?

e) If a dielectric material with a dielectric constant k=3.2 is inserted between the plates, what is the resulting capacitance?

f) What is the potential difference between the plates after the dielectric material is inserted?

Explanation / Answer

(a) The electric field at a point out side the region = 0 N/C (b) The electric field between the plates   E   = /_0 here      = surface charge density   = charge / area =   13*10^-6 / 1.00 m^2 = 13.0*10^-6 N/m^2 /C _0 = 8.85*10^-12 C^2 /N.m^2 E = (13.0*10^-6 N/m^2 /C)/ 8.85*10^-12 C^2 /N.m^2    = 1.47*10^6 N/C (c) Potential difference between the plates V _0 = E * distance between th plates = (1.47*10^6 N/C)*(1.20*10^-3 m) V_0 = 1.764*10^3 V (d) capacitence  C _0 = Q/ V _0 =( 13*10^-6 )/( 1.764*10^3 V) = 7.4*10^-9 F = 7.4pF (e) capacitence with the dielectric C =k*C_0 = 3.2*7.4pF   = 23.68*pF (f) potential difference between the plates after the dielectic is placed V = V_0 / k   =  1.764*10^3 V / 3.2 = 0.55*10^3 V

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