Plot the lines of the electric field between a small point charge

[galipop]

I've been asked to complete electric field E and potential V inside and outside of a simple plate capacitor (the plates are infinitely large and the distance between the two plates is d.)

My working is as follows.

Inside the cap-
$$E = \frac{ \sigma } { \epsilon_{o} }$$

then potential V=Ed

Outside the cap
E=0
V=0

does this seem to cover the question, or am I missing something?

Also I need to plot the lines of the electric field between a small point charge (+) and a large metal plate (charge -)...
for this I'm guessing the lines of the charge leave the charge going straight to the plate, correct?

 

[Gokul43201]

I can't see your LaTeX (there's a temporary problem with displaying LaTeX), but for the first part, your result is essentially correct. But the way to go about it would be to start with the electric field due to an infinite charged plate (sheet, wall, whatever).

For (2), your answer is incorrect. This is essentially a superposition problem. First draw the field lines for a single charge. Then draw them for a charged plate. Now combine the two.

 

[galipop]

Thanks for the reply!

Can you expand a bit more on starting with an electric field due to an infinite charged plate?

 

[galipop]

anyone? .

 

[HallsofIvy]

Imagine a point charge, q, at height l above the plane that has charge density δ. Take the point directly beneath the point charge as the origin of a polar coordinate system. Use polar coordinates since all points on a circle of radius r will have the same force on q: Their horizontal components cancel and their vertical components add. Taking a ring of radius r and width dr, the total area is 2π rdr so the charge is 2πδr dr. The straight line distance from q to a point on that circle is L= √(l²+ r²) so the vertical component of the total force from that ring is (2qπδ/L²)(l/L)= 2qπδl/L^{3. Integrate that with respect to r (don't forget that L is not a constant- it depends on r) from r= 0 to r= infinity.}