Two protons in a molecule are 4.00*10^-10 m apart. Find the electric force exerted by one proton on the other.

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(a) Two protons in a molecule are 4.00 image 10-10 m apart. Find the electric force exerted by one proton on the other.

magnitude N
direction  

(b) State how the magnitude of this force compares with the magnitude of the gravitational force exerted by one proton on the other.

Fe
Fg

=

(c) What must be a particle's charge-to-mass ratio if the magnitude of the gravitational force between two of these particles is equal to the magnitude of electric force between them?
C/kg

asked Jan 15, 2012 in Physics by Roar3215 ~Expert~ (1,318 points)
edited Feb 5, 2012 by pokemonmaster
    

1 Answer

+1 vote
 
Best answer

Part A: to find the electric force exerted use Colulomb's Law, which gives the following formula:   

 
F = k_\mathrm{e} \frac{q_1q_2}{r^2}
ke=8.98*10^9 N*m^2/C^2
 
q1 and q2 are the charge of the proton, which is 1.602*10^-19 C
 
and r is the distance between the two particles which is given in the equation: 4.00 image 10-10 m
 
Now plug these values into the equation and solve to get:
1.44*10^-9 N
 
 
 
 
 
Now for Part B you are comparing the ratio of the electric force to the gravitational force, which is given by the formula below:
 
F = G \frac{m_1 m_2}{r^2}\
 
where G is your gravitational constant which equals: 6.674*10^-11 N*m^2/kg^2
 
and m1 and m2 are the mass of the particles which are each: 1.673*10^-27kg
 
and r is once again 4.00 image 10-10 m. 
 
The gravitational force is found to be: 1.1675*10^-45 N
 
Now the ratio would just be your answer from Part A divided by 1.1675*10^-45 N, which would result in 1.23*10^36 as the answer.
 
 
Lastly, for Part C you are finding the ratio of the charge to the mass, or q/m.
 
To do this set the equations for the gravitational force equal to the equation for the electric force as follows:
 
Fg=Fe
 
(G*m1m2)/r^2 = (ke*q1q2)/r^2
 
now move the variables around until you have a ratio of q/m,
hence:
 
(q/m)=(G/ke)^(1/2)
 
q/m = 8.61753*10^-11
answered Jan 17, 2012 by kirby ~Expert~ (3,020 points)
selected Jan 20, 2012 by Roar3215

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