Q. 49 Metal sphere 1 has a positive ch... [FREE SOLUTION]

Chapter 26: Q. 49 (page 739)

Metal sphere 1 has a positive charge of 6.0 nC. Metal sphere 2, which is twice the diameter of sphere 1, is initially uncharged. The spheres are then connected together by a long, thin metal wire. What are the final charges on each sphere?

Short Answer

Expert verified

The final charges on each sphere is $2 n C$ and $4 n C$ respectively.

Step by step solution

Given Information

We have given that the Metal sphere $1$ has a positive charge of $6.0 n C$ . Metal sphere $2$ , which is twice the diameter of sphere $1$ , is initially uncharged.

Simplify

Two spheres are connected which means the potential is the same in both of them. so, consider this potential as if it came from a point-charge in the middle of the spheres. and equality of potential have

$\frac{k q_{1}}{r_{1}} = V = \frac{k q_{2_{}}}{r_{2}},$

The following relation exists between the charges

$\frac{q_{2} = \frac{r_{2}}{r_{1}} q_{1 .}}{}$

The relation of the sphere radii and that is

$q_{1} + q_{2} = 6 n C$

From the ratio of radii

$q_{2} + 2_{q_{1,}}$

Substitute it to

$q_{1} + 2_{q_{1}} = 6 n C$

It is clear that the charges are

$q_{1} = 2 n C, q_{2} = 4 n C .$

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Metal sphere 1 has a positive charge of 6.0 nC. Metal sphere 2, which is twice the diameter of sphere 1, is initially uncharged. The spheres are then connected together by a long, thin metal wire. What are the final charges on each sphere?

Short Answer

Step by step solution

Given Information

Simplify

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