How many electrons woul be required?

Question

Can someone please solve these step by step?
How many electrons would be required to have a totalk charge of 1.00C on a sphere? assuming the force between 2 spheres is 48 N, what will be the magnitude of the force if the distance between them is doubled?

Answer 1

Part 1) 1 electron=1.62*10^-19 C
1.00 C = [1/(1.62*10^-19)]
=6.1728*10^18 electrons.

Part 2) Formula for force = (9*10^9)*(q1*q2)*(1/r^2)

Since Coloumb's constant and q1*q2 are constants, it is actually,
k/r^2=force, where k=Coloumb's constant+q1*q2.

r^2 and the force are inversely proportional to each other, so when the distance is doubled it is actually,
let the new distance=2r.
(2r)^2= 4r^2.

Thus the force also decreases by 4 times = 12 N

Answer 2

By definition a coulomb ~ 6.25 X 10^18 elementary charges (e.g., electrons).

By Coulomb's Law, we have F ~ qq/r"2 and f ~ qq/R^2; where the q's are the charges (i.e., 1 Coulomb), and the r and R are the distances R > r.

Thus we have F/f = qq/r^2//qq/R^2; st, F/R^2 = f/r^2 and f = F(r/R)^2. If F = 48 N and R = 2r; then f = 48(1/2)^2 = 48/4 = 12 N.

Answer 3

Let x = number of electrons required.
Charge of each electron = 1.60 x 10^(-19) C.
Charge of x electrons
= x * 1.60 x 10^(-19) = 1 C
=> x = 1 / [1.6 x 10^(-19)] = 6.25 x 10^18

Force is inversely proportional to the square of the distance.
So, on doubling the distance force will be one-fourth, i.e.,
48/4 = 12 N.

Answer 4

1)

charge = no. of electrons*charge of an electron

1=no. of electrons*1.6*10^-19

no. of electrons = 1/[1.6*10^-19]

=0.625*10^19

=6.25*10^18 electrons

2)
Force is inversely proportional to the square of the distance between the spheres.

If the distance is r, on doubling it becomes 2r.
Square of 2r is 4(r^2).

Force before doubling (48) is inversely proportional to r^2

After doubling, force (F') is inversely proportional to 4r^2

48/F' = 4r^2/r^2

F' = 48/4

Force after doubling the distance is 12 N

:)

Answer 5

Divide the magnitude by the distance.

1.00 x 48 = 48
divide by 2
48/2 = 24

then times by double 24

24 x 24 = 578 N