The space between the plates of a parallel-plate capacitor of plate area is…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

The space between the plates of a parallel-plate capacitor of plate area

A

is completely filled by two dielectric slabs placed one after the other (in the direction of the field). The first slab has thickness

d_1

and relative permittivity

\kappa_1

, while the second slab has thickness

d_2

and relative permittivity

\kappa_2

. (a) Derive an expression for the effective capacitance of the arrangement in terms of

\varepsilon_0,\,A,\,d_1,\,d_2,\,\kappa_1

and

\kappa_2

. (b) Show that if

\kappa_1 = \kappa_2

, the expression reduces to that of a single slab of thickness

(d_1+d_2)

. (c) For

A = 150\,\text{cm}^2

d_1 = 0.5\,\text{mm}

d_2 = 0.8\,\text{mm}

\kappa_1 = 4

and

\kappa_2 = 6

, compute the numerical value of the capacitance.