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Chapter 26: Q. 73 (page 741)

Derive Equation 26.33 for the induced surface charge density on the dielectric in a capacitor.

Short Answer

Expert verified

By deriving equation 26.33 for the induced surface charge density on the dielectric in a capacitor we get 畏i=1-1魏畏0.

Step by step solution

01

Given Information

Equation 26.33:

畏induced=畏01-1魏

畏inducedranges from nearly zero when 魏鈮�1 to 鈮�畏0 when 魏鈮�1.

02

Explanation

From expression 26.29 we have

Ei=E0-E.

The induced field will be

Ei=畏i蔚0.

Substitute expression 26.30 to 26.26,

魏:=E0E鈬�E0=魏E0,

Now find

localid="1648710646958" Ei=E0-E=E(魏-1)=魏-1魏E0.

The induced charge density will be related to the induced field as

畏i=Ei蔚0

Substituting the previous result,

localid="1648710633563" 畏i=魏-1魏E0蔚0

Note that E0蔚0=畏0and rearrange the ratio, to find the result as in the book:

畏i=1-1魏畏0

03

Final Answer

Hence, the expression will be畏i=1-1魏畏0.

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