- #1

DivGradCurl

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(a) What is the magnitude of the electric field at a radial distance of 3.5 cm from the axis of the cylinder?

Gauss' Law:

[tex]\Phi _{\mbox{Net}} = \oint \vec{E} \cdot d\vec{S} = \int _{\mbox{Sides}} \vec{E} \cdot d\vec{S} = ES =\frac{Q_{\mbox{Enc}}}{\epsilon _0} [/tex]

Let a = 3.5 cm. Then:

[tex]E\left( 2\pi a L \right)=\frac{\rho \left( \pi a^ 2 L \right)}{\epsilon _0} \Longrightarrow E = \frac{\rho a}{2\epsilon _0} = \frac{Aa^ 3}{2\epsilon _0} \approx 7.3 \mbox{ } \frac{N}{C}[/tex]

**This is wrong, but I don't know where.**

(b) What is the magnitude of the electric field at a radial distance of 5.5 cm from the axis of the cylinder?

Gauss' Law:

Let b = 5.5 cm. Then:

[tex]\Phi _{\mbox{Net}} = \oint \vec{E} \cdot d\vec{S} = \int _{\mbox{Sides}} \vec{E} \cdot d\vec{S} = ES =\frac{Q_{\mbox{Enc}}}{\epsilon _0} [/tex]

[tex]E\left( 2\pi b L \right)=\frac{\rho \left( \pi R^ 2 L \right)}{\epsilon _0} \Longrightarrow E = \frac{\rho R^2}{2b\epsilon _0} = \frac{AR^ 4}{2b\epsilon _0} \approx 1.3 \times 10 \mbox{ } \frac{N}{C}[/tex]

**This is wrong, but I don't know where.**

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**Any help is highly appreciated**