Remarks The gravitational force between the charged constituents of the atom is negligible compared with the electric force between them. The electric force is so strong, however, that any net charge on an object quickly attracts nearby opposite charges, neutralizing the object. As a result, gravity plays a greater role in the mechanics of moving objects in everyday life.
Question If the distance between two charges is doubled, by what factor is the magnitude of the electric force changed?
1 .
Examine the dependence of the electrical force in Coulomb's law on the distance r between the two charges. If r is doubled, how does that affect the value of the force? .PRACTICE IT .Use the worked example above to help you solve this problem. The electron and proton of a hydrogen atom are separated by a distance of about 5.87 10-11 m at some instant.
(a) Find the magnitudes of the electric force and the gravitational force that each particle exerts on the other, and the ratio of the electric force, Fe, to the gravitational force, Fg. Fe = 2 N
Fg = 3 N
Fe/Fg = 4
(b) Compute the acceleration caused by the electric force of the proton on the electron. Repeat for the gravitational acceleration. ae = 5 m/s2
ag = 6 m/s2
.EXERCISE HINTS: GETTING STARTED | I'M STUCK! .(a) Find the magnitude of the electric force between two protons separated by 1 femtometer (10−15 m), approximately the distance between two protons in the nucleus of a helium atom.
7 N
(b) If the protons were not held together by the strong nuclear force, what would be their initial acceleration due to the electric force between them?
8 . m/s2 .
Object A attracts object B with a gravitational force of 10 newtons from a given distance. If the distance between the two objects is doubled, what is the changed force of attraction between them?
To find the factor by which the magnitude of the electric force changes when the distance between two charges is doubled, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Mathematically, Coulomb's Law can be expressed as:
F = k * (q1 * q2) / r^2
Where:
F is the magnitude of the electric force
k is Coulomb's constant (approximately equal to 9 * 10^9 N m^2/C^2)
q1 and q2 are the charges of the two objects
r is the distance between the charges
If we double the distance (r) between the charges, it means the new distance (2r) is twice the original distance.
To find the factor by which the magnitude of the electric force changes, we can substitute the new distance (2r) into Coulomb's Law and compare it to the original force (F) when the distance was r.
Let's call the original force F1 and the new force F2. Using Coulomb's Law, we have:
F1 = k * (q1 * q2) / r^2
F2 = k * (q1 * q2) / (2r)^2
Now, let's simplify F2:
F2 = k * (q1 * q2) / 4r^2
To find the factor by which the magnitude of the electric force changes, we can divide F2 by F1:
F2/F1 = (k * (q1 * q2) / 4r^2) / (k * (q1 * q2) / r^2)
= (k * (q1 * q2) / 4r^2) * (r^2 / (k * (q1 * q2))
= 1/4
Therefore, the factor by which the magnitude of the electric force changes when the distance between two charges is doubled is 1/4.