Question

The radius of solid metallic non-conducting sphere is $60 \,cm$ and charge on the sphere is $ 500\,\mu C $ . The electric field at a distance $10\, cm$ from centre of sphere is:

• A. $ 2\times {{10}^{6}}\,N/C $
• B. $ 2\times {{10}^{8}}\,N/C $
• C. $ 5\times {{10}^{6}}\,N/C $
• D. $ 5\times {{10}^{8}}\,N/C $

Answer 1

Answer: (A)

The point $10 \,cm$ from centre of sphere will be inside the sphere. Hence,
$ {{E}_{inside}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{qr}{{{R}^{3}}} $ e
Here, $ q=500\times {{10}^{-6}}C,\,r=10\,cm\,=0.1\,m $
$ R=60\,cm=0.60\,m $
$ \therefore $ $ {{E}_{inside}}=(9.0\times {{10}^{9}})\times \frac{500\times {{10}^{-6}}\times 0.1}{{{(0.60)}^{3}}} $
$ =2\times {{10}^{6}}\,N/C $