- #1

- 21

- 0

**Electricity, Electric Force, and Charge Transfer**

## Homework Statement

"Two conducting spheres have identical radii. Initially, they have charges of opposite sign and unequal magnitudes with the magnitude of the positive charge larger than the magnitude of the negative charge. They attract each other with a force of 0.224 N when separated by 0.4 m.

The spheres are suddenly connected with a thin wire, which is then removed. Now the spheres repel each other with a force of 0.039 N. What are the magnitudes of the initial positive and negative charges? Answer in units of C."

**Given:**

[tex]\bullet F_{e,i} = -0.224 N[/tex]

[tex]\bullet r = 0.4 m[/tex]

[tex]\bullet F_{e,f} = 0.039 N[/tex]

[tex]\bullet k_{C} = 8.99 \times 10^9 \frac{N \cdot m^2}{C^2}[/tex]

**Unknown:**

[tex]\bullet q_{pos} = ? [/tex]

[tex]\bullet q_{neg} = ? [/tex]

## Homework Equations

[tex]F_{e} = \frac{k_{C}q_{1}q_{2}}{r^2}[/tex]

## The Attempt at a Solution

[tex]q_{pos} + q_{neg} = 2 q_{f}[/tex]

[tex]F_{e,i} = \frac{k_{C}q_{pos}q_{neg}}{r^2}[/tex]

[tex]F_{e,f} = \frac{k_{C}q_{f}^2}{r^2}[/tex]

[tex]q_{f} = \sqrt{\frac{F_{e,f}r^2}{k_{C}}} = \frac {q_{pos} + q_{neg}}{2}[/tex]

[tex]q_{pos}+q_{neg} = 2r\sqrt{\frac{F_{e,f}}{k_{C}}[/tex]

[tex]q_{pos} = 2r\sqrt{\frac{F_{e,f}}{k_{C}}}- q_{neg}[/tex]

At this point, I wasn't sure how to go about finding either of these charges, because you need one to solve for the other. Is there some clever mathematical trick or physical concept I'm missing here?

Last edited: