Question

NO Date To find the field $ \vec{E} $ \[ \begin{array}{l} E=-\vec{\nabla} V=-\frac{Q}{2 \pi \epsilon_{0} a^{2}} \frac{d}{d z}\left(\sqrt{z^{2}+a^{2}}-z\right) \hat{k} \\ \left\{-\frac{Q}{2 \pi \epsilon_{0} a^{2}}\left(\frac{z}{\sqrt{z^{2}+a^{2}}}-1\right) \hat{k}\right\} \\ a t \quad z=0 \Rightarrow V=\frac{Q}{2 \pi \epsilon_{0} a}, \vec{E}=\frac{Q}{2 \pi \epsilon_{0} a^{2}} \hat{k} \end{array} \]

          NO
Date

To find the field \( \vec{E} \)
\[
\begin{array}{l}
E=-\vec{\nabla} V=-\frac{Q}{2 \pi \epsilon_{0} a^{2}} \frac{d}{d z}\left(\sqrt{z^{2}+a^{2}}-z\right) \hat{k} \\
\left\{-\frac{Q}{2 \pi \epsilon_{0} a^{2}}\left(\frac{z}{\sqrt{z^{2}+a^{2}}}-1\right) \hat{k}\right\} \\
a t \quad z=0 \Rightarrow V=\frac{Q}{2 \pi \epsilon_{0} a}, \vec{E}=\frac{Q}{2 \pi \epsilon_{0} a^{2}} \hat{k}
\end{array}
\]

$NO Date To find the field E⃗ E=-∇⃗ V=-(Q)/(2 πϵ0 a^2)(d)/(d z)(√(z^2+a^2)-z) k̂ {-(Q)/(2 πϵ0 a^2)((z)/(√(z^2+a^2))-1) k̂} a t z=0 ⇒ V=(Q)/(2 πϵ0 a), E⃗=(Q)/(2 πϵ0 a^2)k̂$

Added by Gregg M.

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