6) An insulating sphere of radius a carries a charge density of k O a. Determine the surface charge density at the inner (r= b) and outer surfaces (r= c) of the conductor. b. Determine the electric field E in all four regions (i) r c. c. Determine the electric potential V at the center of the sphere using infinity (r=oo) as a reference point. in the region r ≤ a, where k is a positive constant and is the distance from the center of the sphere. The sphere is surrounded by a thick, concentric conducting metal shell with an inner radius b and an outer radius c. The conducting shell carries no net charge. Conductor Vacuum d. If the outer shell is grounded, what would the potential at the center of the sphere be using the same reference point as in part (c). Insulator
6) An insulating sphere of radius a carries a charge density of k O a. Determine the surface charge density at the inner (r= b) and outer surfaces (r= c) of the conductor. b. Determine the electric field E in all four regions (i) r c. c. Determine the electric potential V at the center of the sphere using infinity (r=oo) as a reference point. in the region r ≤ a, where k is a positive constant and is the distance from the center of the sphere. The sphere is surrounded by a thick, concentric conducting metal shell with an inner radius b and an outer radius c. The conducting shell carries no net charge. Conductor Vacuum d. If the outer shell is grounded, what would the potential at the center of the sphere be using the same reference point as in part (c). Insulator
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Transcribed Image Text:6) An insulating sphere of radius a carries a charge density of
k
p=
in the region r ≤ a, where k is a positive constant
and is the distance from the center of the sphere. The
sphere is surrounded by a thick, concentric
conducting metal shell with an inner radius b and an
outer radius c. The conducting shell carries no net
charge.
a.
O
Conductor
-Vacuum
Determine the surface charge density at the inner
(r= b) and outer surfaces (r= c) of the conductor.
b.
Determine the electric field E in all four regions (i) r<a, (ii) a <r<b,
(iii) b<r<c, and (iv) r> c.
c. Determine the electric potential V at the center of the sphere using infinity
(r = ∞o) as a reference point.
d.
If the outer shell is grounded, what would the potential at the center of the sphere
be using the same reference point as in part (c).
Insulator
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Step 1: Determine the given data:
VIEWStep 2: Determine the total charge inside the inner sphere:
VIEWStep 3: a. Determine the surface charge density at the inner and outer surface of conductor:
VIEWStep 4: b) (i) Determine the electric field at r<a:
VIEWStep 5: (ii) Determine the electric field at a<r<b:
VIEWStep 6: (iii) Determine the electric field at b<r<c:
VIEWStep 7: (iv) Determine the electric field at r>c:
VIEWStep 8: c) Electric potential V at the center of the sphere:
VIEWStep 9: Check the guideline term:
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