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 :

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
= - $${{\sigma  \over {2{\varepsilon _0}}}\cos 60^\circ \widehat x}$$ + $$\left( {{\sigma  \over {2{\varepsilon _0}}} - {\sigma  \over {2{\varepsilon _0}}}\sin 60^\circ } ight)\widehat y$$
= $${ - {\sigma  \over {4{\varepsilon _0}}}\widehat x}$$ + $${\sigma  \over {2{\varepsilon _0}}}\left( {1 - {{\sqrt 3 } \over 2}} ight)\widehat y$$
= $${\sigma  \over {2{ \in _0}}}\left[ {\left( {1 - {{\sqrt 3 } \over 2}} ight)\widehat y - {{\widehat x} \over 2}} ight]$$

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: