Question

An electron is in a vacuum near Earth's surface and located at y = 0 m on a vertical y axis. At what value of y should a group of 23 electrons be placed such that its electrostatic force on the first electron balances the gravitational force on the first electron?

Answer 1

To balance the gravitational and electrostatic forces on an electron near Earth's surface, you need to calculate both forces and equate them. The gravitational force is the product of the electron's mass and the gravitational acceleration. The electrostatic force is determined using Coulomb's law for 23 electrons, and by setting these equal, you can solve for the required distance, y.

Step-by-step explanation:

To find at what value of y a group of 23 electrons should be placed to balance the gravitational force on the first electron, we need to calculate the gravitational force and the electrostatic force acting on the electron and set them equal.

The gravitational force (Fg) on an electron with mass (me) near Earth's surface can be calculated using Newton's second law of gravitation: Fg = meg, where g is the acceleration due to gravity (approximately 9.81 m/s2).

The electrostatic force (Fe) between two point charges is given by Coulomb's law: Fe = kq1q2/r2, where k is Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them.

By setting Fg equal to Fe, we solve for y with 23 times the charge of an electron since there are 23 electrons. Thus:
meg = 23kqe^2/y2

Solving for y, we get:
y = sqrt(23kqe^2/(meg))

Answer 2

the bunch of 23 electrons must be placed on y axis at coordinate y = - 24.35 m.

Step-by-step explanation:

As we know that the gravitational force on electron at y = 0 is counter-balanced by the weight of the electron

So we have

`(kq_1q_2)/(r^2) = mg`

here we have

`q_1 = e`

`q_2 = 23 e`

`m = 9.11 * 10^(-31) kg`

also we know that

`e = 1.6 * 10^(-19) C`

so we will have

`((9* 10^9)(1.6 * 10^(-19))(23* 1.6 * 10^(-19)))/(r^2) = (9.11 * 10^(-31))(9.81)`

`(5.3 * 10^(-27))/(r^2) = 8.94 * 10^(-30)`

`r = 24.35 m`

so the bunch of 23 electrons must be placed on y axis at coordinate y = - 24.35 m.