Question

Compute the size of the charge necessary for two spheres separated by 1m to be attached with the force of 1N. How many electrons is this charge?

Answer 1

`q\approx 6.6\cdot 10^(13)~electrons`

Step-by-step explanation:

Coulomb's Law

The force between two charged particles of charges q1 and q2 separated by a distance d is given by the Coulomb's Law formula:

`\displaystyle F=k(q_1q_2)/(d^2)`

Where:

`k=9\cdot 10^9\ N.m^2/c^2`

q1, q2 = the objects' charge

d= The distance between the objects

We know both charges are identical, i.e. q1=q2=q. This reduces the formula to:

`\displaystyle F=k(q^2)/(d^2)`

Since we know the force F=1 N and the distance d=1 m, let's find the common charge of the spheres solving for q:

`\displaystyle q=\sqrt{(F)/(k)}\cdot d`

Substituting values:

`\displaystyle q=\sqrt{(1)/(9\cdot 10^9)}\cdot 1`

`q = 1.05\cdot 10^(-5)~c`

This charge corresponds to a number of electrons given by the elementary charge of the electron:

`q_e=1.6 \cdot 10^(-19)~c`

Thus, the charge of any of the spheres is:

`\displaystyle q = (1.05\cdot 10^(-5)~c)/(1.6 \cdot 10^(-19)~c)`

`\mathbf{q\approx 6.6\cdot 10^(13)~electrons}`