Question
Three infinitely long charge sheets are placed as shown in figure. The electric field at point $$P$$ is
Three infinitely long charge sheets are placed as shown in figure. The electric field at point $$P$$ is
A.
$$\frac{{2\sigma }}{{{\varepsilon _0}}}\hat k$$
B.
$$\frac{{4\sigma }}{{{\varepsilon _0}}}\hat k$$
C.
$$ - \frac{{2\sigma }}{{{\varepsilon _0}}}\hat k$$
D.
$$ - \frac{{4\sigma }}{{{\varepsilon _0}}}\hat k$$
Answer :
$$ - \frac{{2\sigma }}{{{\varepsilon _0}}}\hat k$$
Solution :
Figure shows the electric fields due to the sheets 1, 2 and 3 at point $$P.$$ The direction of electric fields are according to the charge on the sheets (away from positively charge sheet and towards the negatively charged sheet and perpendicular).
The total electric field
$$\eqalign{ & \vec E = {{\vec E}_1} + {{\vec E}_2} + {{\vec E}_3} \cr & = {E_1}( - \hat k) + {E_2}( - \hat k) + {E_3}( - \hat k) \cr & = \left[ {\frac{\sigma }{{2{\varepsilon _0}}} + \frac{{2\sigma }}{{2{\varepsilon _0}}} + \frac{\sigma }{{2{\varepsilon _0}}}} \right]( - \hat k) = - \frac{{2\sigma }}{{{\varepsilon _0}}}\hat k \cr} $$
Figure shows the electric fields due to the sheets 1, 2 and 3 at point $$P.$$ The direction of electric fields are according to the charge on the sheets (away from positively charge sheet and towards the negatively charged sheet and perpendicular).
The total electric field
$$\eqalign{ & \vec E = {{\vec E}_1} + {{\vec E}_2} + {{\vec E}_3} \cr & = {E_1}( - \hat k) + {E_2}( - \hat k) + {E_3}( - \hat k) \cr & = \left[ {\frac{\sigma }{{2{\varepsilon _0}}} + \frac{{2\sigma }}{{2{\varepsilon _0}}} + \frac{\sigma }{{2{\varepsilon _0}}}} \right]( - \hat k) = - \frac{{2\sigma }}{{{\varepsilon _0}}}\hat k \cr} $$
