If the permittivities are nearly the same, so that is small, the qualitative approach to…

If the permittivities are nearly the same, so that e7763a3f 781d 4912 bfa1 53511fee4414 is small, the qualitative approach to determining the field distribution given in connection with Fig. 6.6.7 can be made quantitative. That is, if b7e4c50a 56a2 4c08 9de2 0ca478b5c3e2 is small, the polarization charge induced by the imposed field can be determined to a good approximation and that charge, in turn, used to find the change in the applied field. Consider the following approximate approach to finding the fields in and around the dielectric cylinder of Example 6.6.2.

(a) In the limit where b7e4c50a 56a2 4c08 9de2 0ca478b5c3e2 is zero, the field is equal to the applied field, both inside and outside the cylinder. Write this field in polar coordinates.

(b) Show that this field gives rise to 4f8ee35c 0ae1 42c0 a273 906e20a154deat the surface of the cylinder.

(c) Find the field due to this induced polarization surface charge and add it to the imposed field to show that, with the first-order contribution of the induced polarization surface charge, the field is

74d0ce0f 08c5 42a0 9391 6e46c8b2e364

(d) Expand the exact fields given by (21) and (22) to first order in b7e4c50a 56a2 4c08 9de2 0ca478b5c3e2 and show that they are in agreement with this result.

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