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- Homework Statement
- Given a linecharge ##p_l## straight across a half-cylinder on a large ground plane, as shown in figure. Determine the magnitude and direction of the force on the line charge per unit length. Also verify that the dimension of the expression is correct. The half-cylinder and the ground plane are both metal and are treated as perfectly conducting

- Relevant Equations
- To get the Electric field ##d\mathbf{E} = \frac{dq'}{4\pi\epsilon_0}\frac{\mathbf{r} - \mathbf{r}'}{\left|\mathbf{r} - \mathbf{r}'\right|^3}##

Lorentz law ##\mathbf{F} = q\mathbf{E}##

Hi,

I want to solve the problem by method of mirroring and by using the electric field by doing superposition and then adding them up to use in Lorentz law to get the force. I have attached a figure that represents the problem.

How do I know from the figure that $-p_l$ is from the half-cylinder and why is it on the positive part of z-axis? The mirroring have opposite direction of $p_l$ depending if its from the linecharge or from the metal half cylinder.

How do I know that the ##-p_l## is on the distance ##z=\frac{a^2}{h}##?

How should I pick my source and field vectors? I believe I should have my field vector as ##r = h \hat{\mathbf{z}}##.

Kind regards,

I want to solve the problem by method of mirroring and by using the electric field by doing superposition and then adding them up to use in Lorentz law to get the force. I have attached a figure that represents the problem.

How do I know from the figure that $-p_l$ is from the half-cylinder and why is it on the positive part of z-axis? The mirroring have opposite direction of $p_l$ depending if its from the linecharge or from the metal half cylinder.

How do I know that the ##-p_l## is on the distance ##z=\frac{a^2}{h}##?

How should I pick my source and field vectors? I believe I should have my field vector as ##r = h \hat{\mathbf{z}}##.

Kind regards,