Question

Assume that the gravitational and the electre foras between two electrons an equal. What must be the mass of the election if the vale of its charge remains unchanged? You will hud the following information: chary of exctron: qe​=−1.6×10−11C Electric constant: k=9×109Nm2/C2 - Gravitational consrant: G=6.67×10−11Nm2/kg2

Answer 1

To find the mass of an electron given that the gravitational and electrical forces between two electrons are equal, we can equate the gravitational force to the electrical force using the respective constants. The equation for the gravitational force is given by Newton's law of gravitation and the equation for the electrical force is given by Coulomb's law. By setting these two forces equal to each other, we can solve for the mass of the electron.

The gravitational force between two electrons is given by:

Fg = G * me2 / r2

The electrical force between two electrons is given by:

Fe = k * qe2 / r2

Setting these two forces equal to each other, we can simplify the equation:

G * me2 / r2 = k * qe2 / r2

Dividing both sides by r2 and rearranging the equation, we get:

me2 = (k * qe2) / G

Taking the square root of both sides, we can solve for the mass of the electron:

me = sqrt((k * qe2) / G)

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