Question

Two spherical objects are separated by a distance of 2.59 × 10-3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result, each object experiences an electrostatic force that has a magnitude of 4.94 × 10-21 N. How many electrons did it take to produce the charge on one of the objects?

Answer 1

Answer:

Number of electrons, n = 12 electron

Explanation:

Given that,

The distance between charged spheres, $d=2.59\times 10^{-3}\ m$

The object experiences an electrostatic force that has a magnitude of, $F=4.94\times 10^{-21}\ N$

The electric force between spheres is given by :

$F=\dfrac{kq^2}{d^2}$

$q=\sqrt{\dfrac{Fd^2}{k}}$

$q=\sqrt{\dfrac{4.94\times 10^{-21}\times (2.59\times 10^{-3})^2}{9\times 10^9}}$

$q=1.91\times 10^{-18}\ C$

Let there are n number of electrons. Using quantization of electric charge we get :

$q=ne$

$n=\dfrac{q}{e}$

$n=\dfrac{1.91\times 10^{-18}}{1.6\times 10^{-19}}$

n = 11.93 electrons

or

n = 12 electrons

Hence, 12 electrons produce the charge on one of the objects.