Electric Field Intensity due to a Uniformly Charged Infinite Conducting Plate:
The basic difference between the non-conducting sheet and conducting sheet is that the charge in a non-conducting sheet remain at a place where the charge is given while the charge in a conducting sheet is spread out in a whole sheet and the electric field inside the conducting sheet is zero.
Value of electric field : In the figure conducting sheet is shown. When the some charge is given to the conducting plate, it get’s distributed on the entire external surface of the conductor. If the plane charge sheet is of uniform thickness and infinite size, then the surface charge density (σ) of the charge being uniform on the entire surface. It is the same at the both surfaces.
Consider a cylindrical surface perpendicular to the sheet with the area of cross-section (s) as shown in figure. On the circular surface of the cylinder P is located.
The total charge enclosed = Σq = σS
By the Gauss’s law
Where \(\hat n\) is the unit vector perpendicular to the sheet from the equation (3). We see that the electric field at any point due to the sheet does not depend upon the distance of the point from the sheet i.er the magnitude of electric field at all the points is equal.
∴ E ∝ r0 ………… (4)
The electric field intensity in any other medium.
∴ E = \(\frac{\sigma}{\varepsilon_{m}}=\frac{\varepsilon}{\varepsilon_{r} \varepsilon_{0}}=\frac{\sigma}{K \varepsilon_{0}}\) ………… (5)
Graph of electric field : The electric field intensity does not depend upon the distance of point from the uniformly charged sheet i.e, it remains the same at all the points. The graph of it is obtained as shown in the figure
