这是一份 Imperial帝国理工大学 PHYS96024作业代写的成功案例
问题 1.
\begin{aligned}
E_{x} &=\int \frac{k \mathrm{dq}}{r^{2}} \
&=\int_{-L / 2}^{L / 2} \frac{k \mathrm{~d} x Q}{L r^{2}} \
&=\frac{k Q}{L} \int_{-L / 2}^{L / 2} \frac{\mathrm{d} x}{(d-x)^{2}}
\end{aligned}
证明 .
\begin{aligned}
E_{x} &=\frac{k Q}{L}\left[\frac{1}{d-x}\right]_{-L / 2}^{L / 2} \
&=\frac{k Q}{L}\left(\frac{1}{d-L / 2}-\frac{1}{d+L / 2}\right) .
\end{aligned}
PHYS96024 COURSE NOTES ：
\begin{aligned}
E &=\int_{0}^{-} 2 \pi \sigma b k a\left(a^{2}+b^{2}\right)^{-3 / 2} \mathrm{~d} b \
&=2 \pi \sigma k a \int_{0} b\left(a^{2}+b^{2}\right)^{-3 / 2} \mathrm{~d} b \
&=2 \pi \sigma k a\left[-\left(a^{2}+b^{2}\right)^{-1 / 2}\right]_{b=0}^{\infty} \
&=2 \pi \sigma k
\end{aligned}