Incomplete question as we have not told to find what quantity.The complete question is here
A spherical capacitor contains a charge of 3.50 nC when connected to a potential difference of 210.0 V. Its plates are separated by vacuum and the inner radius of the outer shell is 5.00 cm.calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.
Answer:
(a) ![C=16.7pF](https://tex.z-dn.net/?f=C%3D16.7pF)
(b) ![r_{a} =3.749cm](https://tex.z-dn.net/?f=r_%7Ba%7D%20%3D3.749cm)
(c)
Explanation:
Given data
![Q=3.50nC\\V=210V\\r_{b}=5.0cm](https://tex.z-dn.net/?f=Q%3D3.50nC%5C%5CV%3D210V%5C%5Cr_%7Bb%7D%3D5.0cm)
For part (a)
The Capacitance given by:
![C=\frac{Q}{V}\\ C=\frac{3.50*10^{-9} C}{210V}\\C=1.6666*10^{-11}F\\or\\C=16.7pF](https://tex.z-dn.net/?f=C%3D%5Cfrac%7BQ%7D%7BV%7D%5C%5C%20C%3D%5Cfrac%7B3.50%2A10%5E%7B-9%7D%20C%7D%7B210V%7D%5C%5CC%3D1.6666%2A10%5E%7B-11%7DF%5C%5Cor%5C%5CC%3D16.7pF)
For part (b)
The Capacitance of coordinates is given as
![C=\frac{4\pi e}{\frac{1}{r_{a} }-\frac{1}{r_{b} } }\\ So\\{\frac{1}{r_{a} }-\frac{1}{r_{b} } }=\frac{4\pi *8.85*10^{-12} }{1.666*10^{-11}}=6.672m^{-1} \\ \frac{1}{r_{a} }=6.672+(1 /0.05)\\\frac{1}{r_{a} }=26.672\\r_{a} =1/26.672\\r_{a} =0.0375m\\r_{a} =3.749cm](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B4%5Cpi%20e%7D%7B%5Cfrac%7B1%7D%7Br_%7Ba%7D%20%7D-%5Cfrac%7B1%7D%7Br_%7Bb%7D%20%7D%20%7D%5C%5C%20So%5C%5C%7B%5Cfrac%7B1%7D%7Br_%7Ba%7D%20%7D-%5Cfrac%7B1%7D%7Br_%7Bb%7D%20%7D%20%7D%3D%5Cfrac%7B4%5Cpi%20%2A8.85%2A10%5E%7B-12%7D%20%7D%7B1.666%2A10%5E%7B-11%7D%7D%3D6.672m%5E%7B-1%7D%20%5C%5C%20%5Cfrac%7B1%7D%7Br_%7Ba%7D%20%7D%3D6.672%2B%281%20%2F0.05%29%5C%5C%5Cfrac%7B1%7D%7Br_%7Ba%7D%20%7D%3D26.672%5C%5Cr_%7Ba%7D%20%3D1%2F26.672%5C%5Cr_%7Ba%7D%20%3D0.0375m%5C%5Cr_%7Ba%7D%20%3D3.749cm)
For part (c)
The electric field according to Gauss Law is given by:
![EA=\frac{Q}{e}\\ E=\frac{Q}{4\pi er_{a}^{2} }=\frac{kQ}{r_{a}^{2}}\\ E=\frac{9*10^{9}*3.50*10^{-9} }{(0.0375m)^{2} }\\ E=2.24*10^{4} N/C](https://tex.z-dn.net/?f=EA%3D%5Cfrac%7BQ%7D%7Be%7D%5C%5C%20E%3D%5Cfrac%7BQ%7D%7B4%5Cpi%20er_%7Ba%7D%5E%7B2%7D%20%20%7D%3D%5Cfrac%7BkQ%7D%7Br_%7Ba%7D%5E%7B2%7D%7D%5C%5C%20%20E%3D%5Cfrac%7B9%2A10%5E%7B9%7D%2A3.50%2A10%5E%7B-9%7D%20%7D%7B%280.0375m%29%5E%7B2%7D%20%7D%5C%5C%20E%3D2.24%2A10%5E%7B4%7D%20N%2FC)
The answer is false your welcome
374848282!,!( rnanxjcifjejzxj