| A charge \[10\,\mu C\] is placed at the centre of a hemisphere of radius R = 10 cm as shown. The electric flux through the hemisphere (in MKS units) is |
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A) \[20\times {{10}^{5}}\]
B) \[10\times {{10}^{5}}\]
C) \[6\times {{10}^{5}}\]
D) \[2\times {{10}^{5}}\]
Correct Answer: C
Solution :
According to Gauss's theorem, Electric flux through the sphere \[=\frac{q}{{{\varepsilon }_{0}}}\]. \[\therefore \]Electric flux through the hemisphere \[=\frac{1}{2}\frac{q}{{{\varepsilon }_{0}}}\] \[=\frac{10\times {{10}^{-6}}}{2\times 8\,.\,854\times {{10}^{-12}}}=0\,.\,56\times {{10}^{6}}\,N{{m}^{2}}{{C}^{-1}}\] \[\approx \,\,0\,.\,6\times {{10}^{6}}\,N{{m}^{2}}{{C}^{-1}}=6\times {{10}^{5}}\,N\,{{m}^{2}}\,{{C}^{-1}}\].
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