Electric field near metal plate

[Keano16]

Homework Statement

An infinite, thin, uniformly charged rod (line charge density lambda) is placed parallel to a metal plate a distance d above it. Calculate the E-field close to the surface of the plate as a function of perpendicular distance to the rod.

Homework Equations

The Attempt at a Solution

I calculated that at a perpendicular distance d away, the E-field of an infinite rod would be (lambda)/(2*pi*epsilon*d). I also realize that the method of images needs to be applied in this case in order calculate the charge induced onto the plate, and that would require me to consider an identical infinite rod at -d from the plate, with a line charge density of -lambda. However, I do not know how to proceed from here, as calculating the total potential keeps giving me 0.


Thanks

 

[ideasrule]

So if there's a negatively charged rod 2d from a positively charged rod, what's the electric field in their middle?

 

[kerimek]

for your question! It seems like you have made some good progress in your calculations so far. To continue, you will need to use the principle of superposition to add the contributions from the original rod and the image rod. This will give you the total electric field at any point near the metal plate.

Additionally, keep in mind that the induced charge on the plate will create its own electric field, which will also contribute to the total electric field near the surface of the plate. You will need to consider both the induced charge and the original charge when calculating the total electric field.

Another approach to this problem could be to use Gauss's law and consider a Gaussian surface close to the surface of the plate. This will allow you to calculate the electric field directly from the charge density on the plate.

I hope this helps guide you in the right direction. Keep up the good work!