two charged spherical conductors R1 = 6cm, R2 = 2cm, are seperated by a distace much greater than 6cm and are connected by a long thin conducting wire. A total charge of Q= +80 nC is placed on one sphere. What is the charge on each sphere?

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Nestor RutherfordLv2

29 Aug 2019

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Consider two conducting spheres with radii R₁ and R₂ separated by a distance much greater than either radius. A total charge Q is shared between the spheres. The total charge Q is equal to q₁ + q₂, where q1 represents the charge on the first sphere and q₂ the charge on the second. Because the spheres are very far apart, you can assume the charge of each is uniformly distributed over its surface. Show that the energy associated with a single conducting sphere of radius R and charge q is surrounded by a vacuum is U = k_eq²/2R.

limedinosaur445

(i) A metallic sphere A of radius 1.00 cm is several centimeters away from a metallic spherical shell B of radius 2.00 cm. Charge 450 nC is placed on A, with no charge on B or anywhere nearby. Next, the two objects are joined by a long, thin, metallic wire (as shown in the figure), and finally the wire is removed. How is the charge shared between A and B?

(a) 0 on A, 450 nC on B

(b) 90.0 nC on A and 360 nC on B, with equal surface charge densities

(d) 225 nC on A and 225 nC on B

(e) 450 nC on A and 0 on B

(ii) A metallic sphere A of radius 1 cm with charge 450 nC hangs on an insulating thread inside an uncharged thin metallic spherical shell B of radius 2 cm. Next, A is made temporarily to touch the inner surface of B. How is the charge then shared between them? Choose from the same possibilities.