Answer:
a) 4.325*10^10 V/m
b) 1.689*10^10 V/m
c) 0
d) 6.384 C/m^3
Explanation:
Hello!
The electric field of a sphere of uniform charge is a piecewise function, let a be the raius of the sphere
For r<a:
[tex]E = kQ\frac{r}{a^{3}}[/tex]
For r>a:
[tex]E=kQ/r^{2}[/tex]
Since a=0.26m and k= 8.987×10⁹ N·m²/C²
a)
[tex]E= 8.987\times10^{9}\frac{0.47C \times0.18m}{(0.26m)^{3}}[/tex]
E=4.325*10^10 V/m
b)
[tex]E= 8.987\times10^{9}\frac{0.47C}{(0.5m)^{2}}[/tex]
E=1.689*10^10 V/m
c)
Since r --> ∞ 1/r^2 --> 0
E(∞)=0
d)
The charge density may be obtained dividing the charge by the volume of the sphere:
[tex]\rho = \frac{Q}{V} =\frac{0.47C}{\frac{4}{3} \pi (0.26m)^{3}}=6.384 C/m^{3}[/tex]
