A) \[\pi {{R}^{2}}E\]
B) \[\sqrt{2}\pi {{R}^{2}}E\]
C) \[\pi {{R}^{2}}E/\sqrt{2}\]
D) None of these
Correct Answer: C
Solution :
[c] \[{{\phi }_{plain}}+{{\phi }_{curve}}=0\text{ or }{{\phi }_{plain}}=-{{\phi }_{curve}}\] \[{{\vec{A}}_{1}}=-\frac{\pi {{R}^{2}}}{2}\hat{i},{{\vec{A}}_{2}}=-\frac{\pi {{R}^{2}}}{2}\hat{j}\] \[\vec{E}=E\cos 45{}^\circ \hat{i}+E\sin 45{}^\circ \hat{j}\] \[=\frac{E}{\sqrt{2}}\hat{i}+\frac{E}{\sqrt{2}}\hat{j}\text{ and }\] \[\phi =\vec{E}.({{\vec{A}}_{1}}+{{\vec{A}}_{2}})\] \[=\frac{-E}{\sqrt{2}}\frac{\pi r{{R}^{2}}}{2}-\frac{E}{\sqrt{2}}\frac{\pi r{{R}^{2}}}{2}=\frac{-\pi {{R}^{2}}E}{\sqrt{2}}\] This is the flux entering. So flux is \[\frac{\pi {{R}^{2}}E}{\sqrt{2}}\]You need to login to perform this action.
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