Question

2. Three infinitely long charge sheets are placed as shown in
figure. Find the E.F at the point P
AZ
O
Z=3a
-20
Z-a
-
Z=-a​

Answer 1

Given:

Three infinitely long charged sheets are placed as shown in the figure.

To find:

Field intensity at point P according to the co-ordinate axes.

Calculation:

The net electrostatic field intensity at point P will be superimposition of the field vectors from the individual charged sheets at point P.

The upper-most plate has positive surface charge density and hence the field intensity of that plate at point P will be directed towards -Z axis.

The middle and lower plate has negative surface charge density hence the field intensity for those plates at point P will also be directed towards -Z axis.

Let net field be $E_{net}$

$\sf{ \therefore\vec{E}_{net} = \dfrac{ \sigma}{ 2\epsilon_{0}} (- \hat{k}) + \dfrac{ 2\sigma}{ 2\epsilon_{0}} (- \hat{k}) + \dfrac{ \sigma}{ 2\epsilon_{0}} (- \hat{k})}$

$\sf{ = > \vec{E}_{net} = \dfrac{ 4\sigma}{ 2\epsilon_{0}} (- \hat{k}) }$

$\sf{ = > \vec{E}_{net} = \dfrac{ 2\sigma}{ \epsilon_{0}} (- \hat{k}) }$

So, final answer is:

$\boxed{ \red{ \large{\rm{\vec{E}_{net} = \dfrac{ 2\sigma}{ \epsilon_{0}} (- \hat{k}) }}}}$