Respuesta :
Answer:
(a) E=0 : 0 cm from the center of the sphere
(b) E= 227.8*10³ N/C : 10.0 cm from the center of the sphere
(c)E= 911.25*10³ N/C : 40.0 cm from the center of the sphere
(d)E= 411.84 * 10³ N/C : 59.5 cm from the center of the sphere
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=16.2 μC=16.2 *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{16.2*10^{-6} }{0.4^{3} } *0.1[/tex]
E= 227.8*10³ N/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}*16.2*10^{-6} }{0.4^{2} }[/tex]
E= 911.25*10³ N/C
(d) Magnitude of the electric field at 59.5 cm from the center of the sphere
r>a , We apply the Formula (1) :
[tex]E=\frac{9*10^{9}*16.2*10^{-6} }{0.595^{2} }[/tex]
E= 411.84 * 10³ N/C
(a) The magnitude of the electric field at a distance of 0 cm from the center of the sphere is 0.
(b) The magnitude of the electric field at a distance of 10 cm from the center of the sphere is 227,812.5 N/C.
(c) The magnitude of the electric field at a distance of 40 cm from the center of the sphere is 911,250 N/C.
(d) The magnitude of the electric field at a distance of 59.5 cm from the center of the sphere is 411,835.32 N/C.
Magnitude of electric field for region inside the sphere
The magnitude of electric field at any given position inside the sphere is calculated using the following formulas;
E = kQr/R³
When the distance , r = 0 cm
E = (kQ x 0)/R³ = 0
When the distance, r = 10 cm
E = (9 x 10⁹ x 16.2 x 10⁻⁶ x 0.1)/(0.4)³
E = 227,812.5 N/C
When the distance, r = 40 cm
E = KQr/R³
r = R
E = kQ/R²
E = (9 x 10⁹ x 16.2 x 10⁻⁶) / (0.4)²
E = 911,250 N/C
Magnitude of electric field for region outside the sphere
The magnitude of electric field at any given position outside the sphere is calculated using the following formulas;
E = kQ/R²
E = (9 x 10⁹ x 16.2 x 10⁻⁶)/(0.595)²
E = 411,835.32 N/C
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