| (i) The electric field at a distance r from the center of the sphere for \[r<a=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{qr}{{{a}^{3}}}\] |
| (ii) The electric field at distance r for \[a<r<b=0\] |
| (iii) The electric field at distane r for \[b<r<c=0\] (iv) The charge on the inner surface of the spherical shell \[=-q\] (v) The charge on the outer surface of the spherical shell \[=+q\] Which of the above statements are true? |
A) (i) (ii) and (v)
B) (i), (iii) and (iv)
C) (ii), (iii) and (iv)
D) (ii), (iii) and (v)
Correct Answer: B
Solution :
The electric field inside the sphere \[{{E}_{Inside}}=\frac{\rho r}{3{{\varepsilon }_{0}}}\] but \[\rho =\frac{q}{\frac{4}{3}\pi {{a}^{3}}}\] \[{{E}_{Inside}}=\frac{q\,\,r}{\frac{4}{3}\pi \,{{a}^{3}}\times 3{{\varepsilon }_{0}}}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}=\frac{qr}{{{a}^{3}}}\] The electric field at distances r for a < r < b is not zero. The electric field at distance r for b < r < c is zero and the charge on the inner surface of the spherical shell is - q. The charge on the outer surface of the spherical shell is zero. Hence the option is correct.
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