**Problem 4.13**An infinitely long cylinder of radius \( a \) carries a uniform polarization \( \mathbf{P} \) (constant in direction, not radial) perpendicular to its axis.(a) Find the electric field inside the cylinder.(b) Show that the field **outside** the cylinder can be expressed in the form:\[\mathbf{E}(s) = \frac{a^2}{2 \varepsilon_0 s^2} \left[ 2 (\mathbf{P} \cdot \hat{s}) \hat{s} - \mathbf{P} \right],\]where \( s \) is the radial coordinate in cylindrical coordinates, and \( \hat{s} \) is the radial unit vector (also in cylindrical coordinates).

(a) Using Gauss law, EA=Qencε0E2πsl=ρVε0E2πsl=ρπs2lε0E→=ρs→2ε0

Answered: An infinitely long cylinder of radius a…

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