Question

How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 4.57×10−21 newtons?

Answer 1

Incomplete question as the spaced between two small spheres is missing.I have assumed 25 cm spaced.The complete question is here

Two small spheres spaced 25.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 4.57×10−21 newtons

Answer:

Each sphere has 1112.02 electrons

Explanation:

Force F=4.57×10⁻²¹N

Space r=25 cm=0.25 m

From Coulombs Law we know that

$F=k\frac{q_{1}q_{2} }{r^{2} }\\ Where\\q_{1}=q_{2}=q\\and\\k=9.0*10^{9}N.m^{2}/C^{2}\\ So\\F=k(q^{2}/r^{2} )\\q=\sqrt{\frac{Fr^{2} }{k} } \\q=\sqrt{\frac{(4.57*10^{-21}N )(0.25m)^{2} }{9.0*10^{9}N.m^{2}/C^{2}}$

q=1.7815×10⁻¹⁶C

After knowing the charge q on sphere we can obtain the number of electrons which is given by:

$n_{e}=\frac{q}{e}\\Where \\e_{electron-charge}=1.602*10^{-19}C/electron \\n_{e}=\frac{(1.7814*10^{-16}C)}{1.602*10^{-19}C/electron}\\n_{e}=1112.02electrons$

Each sphere has 1112.02 electrons