A) \[\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1+\sqrt{3} \right)\hat{y}+\frac{{\hat{x}}}{2} \right]\]
B) \[\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1+\sqrt{3} \right)\hat{y}-\frac{{\hat{x}}}{2} \right]\]
C) \[\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1-\frac{\sqrt{3}}{2} \right)\hat{y}-\frac{{\hat{x}}}{2} \right]\]
D) \[\frac{\sigma }{{{\varepsilon }_{0}}}\left[ \left( 1+\frac{\sqrt{3}}{2} \right)\hat{y}+\frac{{\hat{x}}}{2} \right]\]
Correct Answer: C
Solution :
[c] \[{{\vec{E}}_{1}}=\frac{\sigma }{2{{\varepsilon }_{0}}}\hat{y}\] \[{{\vec{E}}_{2}}=\frac{\sigma }{2{{\varepsilon }_{0}}}(-cos60{}^\circ \hat{x}-\sin 60{}^\circ \hat{y})\] \[=\frac{\sigma }{2{{\varepsilon }_{0}}}\left( -\frac{1}{2}\hat{x}-\frac{\sqrt{3}}{2}\hat{y} \right)\] \[\therefore \overrightarrow{{{E}_{P}}}=\overrightarrow{{{E}_{1}}}+\overrightarrow{{{E}_{2}}}=\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ -\frac{1}{2}\hat{x}+\left( 1-\frac{\sqrt{3}}{2} \right)\hat{y} \right]\]You need to login to perform this action.
You will be redirected in
3 sec