Answer:
(a)Magnitude of the electric field at 0 cm from the center of the sphere:
E=0
(b) Magnitude of the electric field at 10.0 cm from the center of the sphere :
E= 244.7 KN/C
(c) Magnitude of the electric field at 40.0 cm from the center of the sphere :
E=978.8 KN/C
(d) Magnitude of the electric field at 71 cm from the center of the sphere :
E=310.7 KN/C
Explanation:
If we have a uniform charge sphere we can use the following formulas to calculate the Electric field due to the charge of the sphere:
[tex]E=\frac{k*Q}{r^{2} }[/tex] : Formula (1) To calculate the electric field in the region outside the sphere r ≥ a
[tex]E: k*\frac{Q}{a^{3} } *r[/tex] :Formula (2) To calculate the electric field in the inner region of the sphere. r ≤ a
Where:
K: coulomb constant
a: sphere radius
Q: Total sphere charge
r : Distance from the center of the sphere to the region where the electric field is calculated
Equivalences
1μC=10⁻⁶C
1cm= 10⁻²m
Data
k= 9*10⁹ N*m²/C²
Q=17.4 μC=17.4 *10⁻⁶C
a= 40 cm = 40*10⁻²m = 0.4m
Problem development
(a)Magnitude of the electric field at 0 cm :
We replace r=0 in the formula (2) , then, E=0
(b) Magnitude of the electric field at 10.0 cm from the center of the sphere
r<a , We apply the Formula (2):
[tex]E=9*10^{9} *\frac{ 17.4*10^{-6} }{0.4^{3} } *0.1[/tex]
E= 244.7 KN/C
(c) Magnitude of the electric field at 40.0 cm from the center of the sphere
r=a, We apply the Formula (1) :
[tex]E=\frac{9*10^{9}*17.4*10^{-6} }{0.4^{2} }[/tex]
E=978.8 KN/C
(d) Magnitude of the electric field at 71 cm from the center of the sphere
r>a , We apply the Formula (1) :
[tex]E= \frac{9*10^{9}*17.4*10^{-6} }{0.71^{2} }[/tex]
E=310.7 KN/C
