A uniformly charged sphere of 80 μC and radius 2 cm is placed in the air. The electric field intensity at a point 20 cm from the center of the sphere is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 1.80\times10^{7}\,\mathrm{N/C} \)
By Gauss's law, outside a uniformly charged sphere the field is the same as if the whole charge were at the centre. The point is at \( r = 20\,\mathrm{cm} \), which is outside the sphere of radius 2 cm, so
\( \displaystyle E = \frac{1}{4\pi\varepsilon_0}\,\frac{q}{r^{2}} \)
\( q = 80\,\mu\mathrm{C} = 80\times10^{-6}\,\mathrm{C} \)
\( r = 20\,\mathrm{cm} = 0.20\,\mathrm{m} \)
\( 1/4\pi\varepsilon_0 = 9\times10^{9}\,\mathrm{N\,m^2\,C^{-2}} \)
\( \displaystyle E = \frac{9\times10^{9} \times 80\times10^{-6}}{(0.20)^{2}} = \frac{7.2\times10^{5}}{0.04} \)
\( \displaystyle E = 1.80\times10^{7}\,\mathrm{N/C} \)