A prototype sensor employs two identical rectangular conducting plates of width (w )…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A prototype sensor employs two identical rectangular conducting plates of width w and total length 2L. The plates are separated by a uniform distance d. The left half of the region between the plates (length L) is completely filled with a dielectric of constant κ1=4.0, while the right half is completely filled with another dielectric of constant κ2=2.0. Edge effects are negligible.
(a) When viewed as an equivalent combination of two capacitive regions, do the two dielectrics behave as capacitors connected in series or in parallel? Justify your answer by referencing how charge and potential difference distribute across the structure.
(b) Derive an algebraic expression for the total capacitance of the device in terms of κ1,κ2,ϵ0,w,L, and d.
(c) Evaluate the capacitance numerically for w=2.0cm,L=3.0cm,d=0.40mm. Express your answer in nanofarads (nF).