Put into contact them

Electricity and Magnetism Level 1

When two metal balls X and Y, apart from each other by a distance of r, were charged by $+10$ C and $-2$ C, respectively, the electric force between them was $F$ . If we put X and Y into contact and then separate them again with a distance of r, what will be the electric force between them?

1.5

F

0.8

F

1.8

F

0.67

F

2 solutions

Anish Puthuraya
Feb 19, 2014

After touching the two spheres,
the charges on them will become same.

Thus,
charge on each sphere $\displaystyle = \frac{10-2}{2} = 4C$

Hence,
Final force $\displaystyle = \frac{4^2}{4\pi\epsilon_o r^2} = \frac{16}{4\pi\epsilon_o r^2}$

Initial Force $\displaystyle = F = \frac{10\cdot 2}{4\pi\epsilon_o r^2} = \frac{20}{4\pi\epsilon_o r^2}$

It is clear that,
Final force $\displaystyle = \frac{16}{20}\times$ (Initial Force) $\displaystyle = \boxed{0.8F}$

rather potential difference becomes '0' after they touch and reach steady state ... electrons stop moving ...... though the the question does not give info. about radii of given charged spheres ... i think the problem creator wanted us assume them equal...

Chitres Guria - 7 years, 1 month ago

Nitin Goyal
Feb 24, 2014

first calculate F F=K(10)(_2)\r^2 after toching them charge will divde equally thus,charge will on each ball=10-2\2=4 its mean now charge on each ball is 4C. now force will be F'=K(4)4\r^2 then the ratio of F&F'=20\16=5\4 F'=4F\5=0.8F

Put into contact them

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