Electric field in a dielectric material

[noblegas]

Homework Statement

A very long cylinder of liner dielectric materil is placed in an otherwise uniform electric field $$<b>E_0</b>$$ . Find the resulting field within the cylinder. (the radius is a , the susceptibililty $$\chi_e$$ and the axis is perpendicular to $$<b>E_0</b>$$)

Homework Equations

The Attempt at a Solution

$$V_in(r,\theta)= \sigma(l=0..infinity)A_l*r^l*P_l(cos(\theta)$$

should I take the derivative of $$V_in$$ with respect to r to obtain the field? Not sure why latex isn't display infiinity but l is supposed to range from zero to infinity

I also know that $$E_0$$ = $$\lambda/(2*\pi*\epsilon_0*a)$$

$$P_0=\epsilon_0*\chi_e*E_0$$ $$P=\epsilon*\chi_e*E$$ ; should I plugged $$\chi_e=P/(E_0*\epsilon_0)$$ into P to get E?

 

[gabbagabbahey]

Why are you using the general solution of Laplace's equation in Spherical coordinates (with azimuthal symmetry), when cylindrical coordinates are more appropriate?

 

[noblegas]

Why are you using the general solution of Laplace's equation in Spherical coordinates (with azimuthal symmetry), when cylindrical coordinates are more appropriate?

You are right. I just realized that. Is my approach to the problem correct? I should not necessarily assume that the length of a very long cylinder is approaching infinity?

 

[gabbagabbahey]

I would assume that the cylinder is infinitely long...Are there any symmetries present (eg. axial, radial, azimuthal etc.)? What is the general solution to Laplace's equation in cylindrical coordinates with these symmetries?