18. (II) A solid metal sphere of radius 3.00 m carries a total charge of -5.50 μC. What is the magnitude of the electric field at a distance from the sphere's center of (a) 0.250 m. (b) 2.90m, (c) 3.10 m, and (d) 8.00 m? How would the answers differ if the sphere were (e) a thin shell, or (f) a solid nonconductor uniformly charged throughout? Step 1: Determine the given variables Radius of metal sphere, r = 3m Total charge carried by sphere, q = -5.50 μC = -5.50 × 106 C Step 2: Calculate magnitude of electric field at different distances from sphere's center (a.) R = 0.250 m Since R therefore this point lies inside the metal sphere. Inside the solid metal sphere charge is zero thus electric field is also zero. That is, E=0N/C (b.) R = 2.90 m Answer In this case also Rr therefore electric field is given by: E = E = k|Q R² (8.99x10°)(5.50×10-6) (3.10)2 E=5.15 x 103 N/C .......... Answer (d.) R = 8 m Since R therefore electric field is given by: k|Q| E R² E = (8.99×10°)(5.50×10-6) (8)2 E = 773 N/C.. . Answer
18. (II) A solid metal sphere of radius 3.00 m carries a total charge of -5.50 μC. What is the magnitude of the electric field at a distance from the sphere's center of (a) 0.250 m. (b) 2.90m, (c) 3.10 m, and (d) 8.00 m? How would the answers differ if the sphere were (e) a thin shell, or (f) a solid nonconductor uniformly charged throughout? Step 1: Determine the given variables Radius of metal sphere, r = 3m Total charge carried by sphere, q = -5.50 μC = -5.50 × 106 C Step 2: Calculate magnitude of electric field at different distances from sphere's center (a.) R = 0.250 m Since R therefore this point lies inside the metal sphere. Inside the solid metal sphere charge is zero thus electric field is also zero. That is, E=0N/C (b.) R = 2.90 m Answer In this case also Rr therefore electric field is given by: E = E = k|Q R² (8.99x10°)(5.50×10-6) (3.10)2 E=5.15 x 103 N/C .......... Answer (d.) R = 8 m Since R therefore electric field is given by: k|Q| E R² E = (8.99×10°)(5.50×10-6) (8)2 E = 773 N/C.. . Answer
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Transcribed Image Text:18. (II) A solid metal sphere of radius 3.00 m carries a total
charge of -5.50 μC. What is the magnitude of the electric
field at a distance from the sphere's center of (a) 0.250 m.
(b) 2.90m, (c) 3.10 m, and (d) 8.00 m? How would the
answers differ if the sphere were (e) a thin shell, or (f) a
solid nonconductor uniformly charged throughout?
Transcribed Image Text:Step 1: Determine the given variables
Radius of metal sphere, r = 3m
Total charge carried by sphere, q
= -5.50 μC = -5.50 × 106 C
Step 2: Calculate magnitude of electric field at
different distances from sphere's center
(a.) R = 0.250 m
Since R
therefore this point lies inside the metal
sphere. Inside the solid metal sphere charge is zero
thus electric field is also zero. That is,
E=0N/C
(b.) R = 2.90 m
Answer
In this case also R<r therefore electric field is
E=0N/C.......
(c.)
R = 3.10 m
. Answer
In this case, R>r therefore electric field is given by:
E =
E =
k|Q
R²
(8.99x10°)(5.50×10-6)
(3.10)2
E=5.15 x 103 N/C .......... Answer
(d.) R = 8 m
Since R therefore electric field is given by:
k|Q|
E
R²
E =
(8.99×10°)(5.50×10-6)
(8)2
E = 773 N/C..
. Answer
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