We want to find the electric field near an infinite charged conducting plane. Ga

Question

We want to find the electric field near an infinite charged conducting plane. Gauss' Law works for any closed surface whatsoever. The art of using it is to match the shape of the Gaussian surface to the symmetry of the problem. The figure shows a Gaussian surface of the variety called a "pillbox, " a cylinder with an arbitrary area A on each end and extending for a height h from the surface. The conductor bears a surface charge density of sigma in [C/m^2]. The left end of the pillbox is buried inside the conductor. By symmetry, the electric field E must be perpendicular to the surface (read that again, and look at the diagram). Always start by writing down Gauss' Law: The left hand side (Ihs) is an integral over the closed surface of the pillbox. Break this into the sum of three integrals: one each for the left end, the right end, and the sides of the cylinder: counterintegral total = integral left end + integral right end + integral sides where only the first is a closed integral. These three pieces make up the closed surface. Now evaluate each of these integrals separately: Left end: integral E middot dA = __________ (easy because E = 0 inside a conductor). Right end: integral E middot dA = ________ (what is the angle between E and A on the right end cap?). Sides: integral E middot dA = _________ (what is the angle between E and A on the right end cap? 90 degree, right?). Sum these to get: counterintegral E middot dA = ____________ Now for the right hand side (rhs). You need the charge enclosed. But all of the charge resides on the surface of the conductor. What is the area of the surface inside the pillbox? How do you get from area A in [m^2] to charge Q in [C] using the information you have? Q_enclosed = ___________ Now set the lhs equal to the rhs (divided by epsilon_o), simplify, and you are done. Put the answer here: EA = therefore E = Notice a funny thing about this formula. It does not involve the distance from the surface. Why do you suppose this is? What assumption was made that leads to this, and when will it break down?

Explanation / Answer

Electric field near the infinite sheet of charge is uniform and perpendicular to plane of the sheet. It's independent of distance from the charged sheet.

This is due to assumption that charge is infinite and area of sheet is also infinite. The parallel components of electric field to plane of the sheet get cancelled due to adjacent elements and components vertical to plane of sheet get add up. As each element is surrounded by elements electric field is uniform.

It breaks down at the edges of sheet.There the electric field is not zero in parallel direction to sheet. There is flux through the surface parallel to surface. E.dS is not equal to zero at ththe edges pallel to sheet.

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