Question 442: Electrostatics & Capacitance

Question

Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30
o
. The electric field in the region shown between them is given by :
![](https://imagex.cdn.examgoal.net/7kd4dk6h9agwe/86402f12-64af-419a-8831-04af9c7a6502/c8f072e0-4c74-11ea-b62d-51ccc5d4afb6/file-7kd4dk6h9agwf-414w.jpg)

Accepted Answer

Electric field due to each sheet is uniform and
equal to E = ${\sigma  \over {2{\varepsilon _0}}}$
$ 	herefore $ Electric field along y direction
= $\left( {{\sigma  \over {2{\varepsilon _0}}} - {\sigma  \over {2{\varepsilon _0}}}\sin 60^\circ } ight)\widehat y$
Also Electric field along x direction
= - ${{\sigma  \over {2{\varepsilon _0}}}\cos 60^\circ \widehat x}$
$ 	herefore $ Now net electric field between plates
= - ${{\sigma  \over {2{\varepsilon _0}}}\cos 60^\circ \widehat x}$ + $\left( {{\sigma  \over {2{\varepsilon _0}}} - {\sigma  \over {2{\varepsilon _0}}}\sin 60^\circ } ight)\widehat y$
= ${ - {\sigma  \over {4{\varepsilon _0}}}\widehat x}$ + ${\sigma  \over {2{\varepsilon _0}}}\left( {1 - {{\sqrt 3 } \over 2}} ight)\widehat y$
= ${\sigma  \over {2{ \in _0}}}\left[ {\left( {1 - {{\sqrt 3 } \over 2}} ight)\widehat y - {{\widehat x} \over 2}} ight]$
![](https://imagex.cdn.examgoal.net/7kd4dk6h9h1e4/3f79413e-7405-4a47-9d23-e3c3a65d02c3/7f9fb8c0-4c75-11ea-b62d-51ccc5d4afb6/file-7kd4dk6h9h1e5-320w.jpg)

Answer

${\sigma  \over {{ \in _0}}}\left[ {\left( {1 + {{\sqrt 3 } \over 2}} \right)\widehat y + {{\widehat x} \over 2}} \right]$

Answer

${\sigma  \over {2{ \in _0}}}\left[ {\left( {1 + \sqrt 3 } \right)\widehat y + {{\widehat x} \over 2}} \right]$

Answer

${\sigma  \over {2{ \in _0}}}\left[ {\left( {1 + \sqrt 3 } \right)\widehat y - {{\widehat x} \over 2}} \right]$

Answer

${\sigma  \over {2{ \in _0}}}\left[ {\left( {1 - {{\sqrt 3 } \over 2}} \right)\widehat y - {{\widehat x} \over 2}} \right]$

Electrostatics & Capacitance

Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30 o . The electric field in the region shown between them is given by :

Choose the correct answer: