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Is this an uncharged conducting sphere? If so, why the field lines inside it, and what direction should the field lines be at the external surface?sergiokapone said:I need to draw electric field lines of sphere in uniform electric field with LaTeX/TikZ. Can anyone show me equation of field lines in polar coordinates?
View attachment 216702
\begin{tikzpicture}
\clip(-4,-3) rectangle (4,3);
\draw[red] (-4,0) -- (4,0);
\foreach \i in {0,0.5,...,3} {
\draw [thick, color=red, domain=0.05:3.1, samples=200, smooth]
plot (xy polar cs:angle=\x r, radius={ (\i-sin(\x r))/(1*sin(\x r)) });
\draw [thick, color=red, domain=0.05:3.1, samples=200, smooth]
plot (xy polar cs:angle=\x r, radius={ (-\i+sin(\x r))/(1*sin(\x r)) });
}
\fill[white, draw=blue] (0,0) circle (1);
\end{tikzpicture}
haruspex said:that I am not sure what the figure of eight inside the sphere represents, or what the field lines are doing there.
But... the same equation would not apply inside, would it?sergiokapone said:I am also not sure, but the nubber 8 inside is the sequence of eqution.
What is the basis for making them parallel inside? Surely those would be distorted by what is going on outside. There is a symmetry here.sergiokapone said:Yes, the same equation would not apply inside. For lines inside I just draw series of parallel lines.
View attachment 216839
You still have not clearly specified the problem. You have explained that the sphere contains dielectric material, but why should there be a surface charge as you describe? If it is a conductor there is no field inside; if an insulator why should there be a surface charge distribution?sergiokapone said:Parallel lines inside is because fileld inside sphere (as well as for every "ellipsoid-like" body) is uniform. It uniform because charge distribution around surface is ##\sigma \propto \cos\phi##. Such distribution governing by boundary conditions and supperppsition of external uniform field and dipole field of sphere.
Electric field lines are imaginary lines that represent the direction and strength of an electric field. They show the path a positive test charge would follow if placed in the electric field.
Electric field lines are drawn by placing a series of arrows in a region of space. The direction of the arrows shows the direction of the electric field, and the length of the arrows represents the strength of the electric field. The arrows are drawn closer together in regions where the electric field is stronger.
When a sphere is placed in a uniform electric field, the electric field lines will curve around the sphere. This is because the sphere causes a distortion in the electric field, creating a region of stronger electric field on one side of the sphere and a weaker electric field on the other side.
Electric field lines are closer together near the sphere because the electric field is stronger in that region. This is due to the fact that the sphere causes a distortion in the electric field, resulting in a higher concentration of electric field lines.
The spacing of electric field lines indicates the strength of the electric field. The closer together the lines are, the stronger the electric field is in that region. Conversely, the farther apart the lines are, the weaker the electric field is in that region.