Question

An electron is released a short distance above earth's surface. a second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel the gravitational force on it. how far below the first electron is the second? the value of coulomb's constant is 8.98755 × 109 n · m2 /c 2 and the acceleration of gravity is 9.81 m/s 2 .

Answer 1

The mass of an electron is 9.109 x 10⁻³¹ kg

The weight of the electron is (mass) x (g) =  8.926 x 10⁻³⁰ Newton

The charge on an electron is -1.602 x 10⁻¹⁹ Coulomb

The repelling force between the two electrons is (K · q₁ · q₂ / r²) =

(8.98755 x 10⁹ N-m²/C²) x (1.602 x 10⁻¹⁹ C)² / D²

In order for the bottom one to just exactly hold the top one up at a distance 'D', the repelling force has to be exactly equal to the weight of the upper electron.

8.926 x 10⁻³⁰ N = (8.98755 x 10⁹ N-m²/C²)·(1.602 x 10⁻¹⁹ C)² / D²

We have to solve THAT ugly mess for ' D '.

Clean up the units first:

Cancel the C² on the right side, then divide each side by Newton:

8.926 x 10⁻³⁰ = (8.98755 x 10⁹ m²) x (1.602 x 10⁻¹⁹)² / D²

Now, let's multiply both sides by (D² x 10²⁹) :

D² x 8.926 x 10⁻¹ = (8.98755 m²) x (1.602)²

Divide each side by (0.8926):

D² = (8.98755 x 1.602²) / (0.8926)  meter²

D² = 25.84 m²

Take the square root of each side:

D = 5.08 meters

I am shocked, impressed, and amazed !

Are you shocked, impressed, or amazed ?