if 3e charge is at the origin and the magnesium nucleus is 3cm from the origin in the +x direction, at what position along the x- axis should an electron be placed so that the electron experiences no net force?

Question

if 3e charge is at the origin and the magnesium nucleus is 3cm from the origin in the +x direction, at what position along the x- axis should an electron be placed so that the electron experiences no net force?

Answer 1

What you are really asking is where to put a 1 e charge to exactly balance a 3 e located charge at the origin if we are standing at x = 3 holding charge q

F/q = k Q1 /r^2
F/q to left = k (-3)/9

F/q to right = k (-1)/(x-3)^2

so
1/(x-3)^2 = 1/3
(x-3)^2 = 3
x-3 = sqrt 3
x = 3 + sqrt 3

Answer 2

To find the position along the x-axis where an electron experiences no net force, we need to calculate the distance from the 3e charge to the electron.

Let's break down the problem:

1. The charge of the magnesium nucleus is 3e, located 3 cm from the origin in the +x direction.
2. We want to find the position along the x-axis where an electron experiences no net force.

To find this position, we can use Coulomb's Law:

F = k * (q1 * q2) / r^2

where:
- F is the force between the two charges,
- k is Coulomb's constant (k ≈ 9 x 10^9 Nm^2/C^2),
- q1 and q2 are the magnitudes of the charges,
- and r is the distance between the charges.

Since both the 3e charge and the electron have opposite charges, their force will be attractive. To have a net force of zero, the magnitudes of the forces on each charge need to be equal. Therefore:

F1 = F2

Now let's substitute the values into the equation:

k * ((3e) * e) / (3 cm + x)^2 = k * (e * e) / (x^2)

where e is the elementary charge (e ≈ 1.6 x 10^-19 C).

Simplifying, we get:

(3 * x)^2 = (3 cm + x)^2

9x^2 = (3 cm + x)^2

Expanding and simplifying, we get:

9x^2 = 9 cm^2 + 6 * 3 cm * x + x^2

8x^2 - 18 cm * x - 9 cm^2 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula.

Factoring: (4x + 3 cm)(2x - 3 cm) = 0

This gives two possible solutions:
1) 4x + 3 cm = 0, or
2) 2x - 3 cm = 0

Solving for x, we get:
1) x = -3 cm / 4 (which is not a valid solution since we are looking for a position along the x-axis),
2) x = 3 cm / 2 = 1.5 cm

Therefore, the electron should be placed at a position of 1.5 cm along the x-axis from the origin to experience no net force.

if 3e charge is at the origin and the magnesium nucleus is 3cm from the origin in the +x direction, at what position along the x- axis should an electron be placed so that the electron experiences no net force?

What you are really asking is where to put a 1 e charge to exactly balance a 3 e located charge at the origin if we are standing at x = 3 holding charge q

IS 1

To find the position along the x-axis where an electron experiences no net force, we need to calculate the distance from the 3e charge to the electron.