Relative to the electrical force between two protons the gravitational force between them is

WIlson B.

asked • 10/25/19

A electric force is much stronger than the gravitational force

B gravitational force is much stronger that the electric force

C electric force is shorter range than the gravitational force

D gravitational force is shorter range than the electric force

1 Expert Answer

William W. answered • 10/25/19

Experienced Tutor and Retired Engineer

Consider the nucleus of a Helium atom (2 protons). The size of the nucleus is about 10-15 m so let's assume that's the distance between the protons as a rough cut. The mass of a proton is 1.7 × 10-27 kilograms. The electrical charge (q) of a proton is 1.6 x 10-19 coulombs.

Gravitational force is calculated by FG = Gm1m2/d2

where G, the Gravitational Constant, is 6.67-11 m3/s2/kg so:

FG = (6.67-11)(1.7 × 10-27)(1.7 × 10-27)/(10-15)2 ≈ 2 x 10-34 N

Electrical force is calculated by FE = kq1q2/d2

where k, Coulomb's constant, is 9 x 109 N m2/C2 so:

FE = (9 x 109)(1.6 x 10-19)(1.6 x 10-19)/(10-15)2 ≈ 200 N

So it's fair to say that the electrical force is MUCH greater than the gravitational force (note that these two forces act in opposite directions)

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