A line charge of length $L$ with uniform density $\lambda_{0}$ is orientated the two ways shown with respect to a grounded sphere of radius $R$. For both cases:
Рис. 1
Рис. 2
1
Consider the incremental charge element $\lambda_{0} \,\mathrm d z^{\prime}$ a distance $r_{Q P}$ from the sphere center. What is its image charge and where is it located?
2
What is the total charge induced on the sphere?
Hint:$$ \int \frac{\mathrm d z^{\prime}}{\sqrt{R^{2}+z^{\prime 2}}}=\ln \left(z^{\prime}+\sqrt{R^{2}+z^{\prime 2}}\right) $$
