Advertisements
Advertisements
प्रश्न
Two parallel uniformly charged infinite plane sheets, '1' and '2', have charge densities + `sigma and -2sigma `respectively. Give the magnitude and direction of the net electric field at a point.
(i) in between the two sheets and
(ii) outside near the sheet '1'.
उत्तर
Which is same in both the case so it is independent of the size and shape of the closed surface
Let `hat6` be the unit vector directed from left to right
Let P and Q are two points in the inner and outer region of two plates respectively charge densities on plates are + `sigma and -2sigma`
(i) Electric field at point P in the inner region of the plates
`vec"E"_1 = sigma/(2epsilon_0) hat"r" and vec"E"_2 = (2sigma)/(2epsilon_0)hat"r"`
∴ Net electric field in the inner region of the plates (i.e., at P) is
`vec"E" = vec"E"_1 vec"E"_2`
`vec"E" = (sigma/(2epsilon_0)+ sigma/epsilon_0)hat"r"`
`vec"E" = (3sigma)/(2epsilon_0)hat"r"`
(ii) Electric field at point Q in the outer region of plate 1
`vec"E"_1 = sigma/(2epsilon_0)(-hat"r") and vec"E"_2 = (2sigma)/(2epsilon_0)hat"r"`
∴ Net electric field in the outer region of plate 1 (i.e. at Q ) is
`vec"E" = vec"E"_1 + vec"E"_2 = (sigma/epsilon_0 - sigma/(2epsilon_0))hat"r"`
`vec"E" = sigma/(2epsilon_0)hat"r"`
APPEARS IN
संबंधित प्रश्न
Derive the expression for the capacitance of a parallel plate capacitor having plate area A and plate separation d.
A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor.
A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved farther apart by pulling them by means of insulating handles, then ______.
Figure shows plot of charge versus potential difference for four parallel plate capacitors, which have same plate area, dielectric medium but different distance between the plates. Which one of them have smallest plate distance?
Capacity of a parallel plate capacitor with a medium of dielectric constant 8 is 12 µF. If the medium is removed, then capacity of the capacitor would be ____________.
Four capacitors of equal capacity have an equivalent capacitance C1 when connected in series and an equivalent capacitance C2 when connected in parallel. The ratio `c_2/c_1`, is ______
A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?
When air replace by dielectric medium of constant K, the maximum force of attraction between two charges separate by a distance.
A dielectric slab of thickness 't’ is kept between the plates of a parallel plate capacitor with plate separation 'd' (t < d). Derive the expression for the capacitance of the capacitor.
