Final answer:
The electromagnetic force between two electrons 2.00 m apart is 2.30 x 10−29 N, and the gravitational force between them is 5.54 x 10−71 N. The ratio of these forces is approximately 4.15 x 10−42.
Step-by-step explanation:
To compare the magnitude of the electromagnetic and gravitational forces between two electrons separated by a distance of 2.00 m, we can use Coulomb's Law for the electromagnetic force (Fe) and Newton's Law of Universal Gravitation for the gravitational force (Fg).
The formula for Coulomb's Law is Fe = k |q1q2| / r2, where k is Coulomb's constant (8.99 x 109 N m2/C2), q1 and q2 are the charges of the electrons (1.61 x 10−19 C), and r is the separation distance (2.00 m).
The gravitational force is given by Newton's Law of Universal Gravitation, which is Fg = G m1m2 / r2, where G is the gravitational constant (6.67 x 10−11 N m2/kg2), and m1 and m2 are the masses of the electrons (9.11 x 10−31 kg).
After calculating these values, we get:
Fe = 2.30 x 10−29 NFg = 5.54 x 10−71 N
To find the ratio Fe/Fg, we divide the electromagnetic force by the gravitational force, resulting in:
Fe/Fg = 4.15 x 1042.