Consider a parallel plate capacitor with a thin dielectric material (er = 3.00)

Question

Consider a parallel plate capacitor with a thin dielectric material (er = 3.00) inserted between the plates. The surface charge density on the plates is 3.00 µC.

(a) Find electric displacement, electric field and polarization outside and inside the dielectric for the region between the plates of the capacitor. Ignore any edge effects.

(b) Find the bound charge.

(c) If the electric displacement is represented by 12 field lines in the region between the plates of the capacitor, how many fields are there for the electric field and polarization inside and outside the dielectric.

(d) Sketch a diagram of the capacitor with the dielectric showing the free and bound charges and the field lines for the electric displacement, electric field and polarization.
(e0= 8.854×10-12 C2.N-1.m-2)

e) Under which condition must more work be done in moving apart the plates of a capacitor:
(1) when the capacitor is connected to the voltage source all the time or
(2) when it is disconnected after the initial charging.
Explain your answer

Thanks in advance!

Explanation / Answer

k = 3.00 sigma = 3.00 uC/m^2 = 3.00 * 10^-6 C/m^2 or q/A = 3.00 * 10^-6 C/m^2 or A = q/3.00 * 10^-6 q is charge on the plates capacitance of capacitor C = e_oA/d e_o = 8.85 * 10^-12 C^2/Nm^2 and d is separation between the plates capacitance with dielectric is C1 = k * C permittivity with dielectric is e = k * e_o

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