Two point charges, q1 and q2, are located at a distance r apart in a vacuum. The electric force between them is F. What will the electric force become if the distance between the charges in tripled?
A. F/9
B. 9F
C. 3F
D. F/3
To determine how the electric force between two point charges changes when the distance between them is tripled, we can use Coulomb's Law.
Coulomb's Law states that the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, Coulomb's Law is expressed as:
F = (k * q1 * q2) / r^2
Where:
F is the electric force between the charges,
k is the Coulomb's constant,
q1 and q2 are the charges of the particles, and
r is the distance between the charges.
If the distance between the charges is tripled, the new distance will be 3r.
Substituting the new distance into Coulomb's Law:
F' = (k * q1 * q2) / (3r)^2
F' = (k * q1 * q2) / 9r^2
Since F' is the electric force with the tripled distance, we can compare it to the original electric force F:
F' / F = ((k * q1 * q2) / 9r^2) / (k * q1 * q2) / r^2
F' / F = (k * q1 * q2 / 9r^2) * (r^2 / k * q1 * q2)
F' / F = 1/9
Therefore, the electric force becomes F/9 if the distance between the charges is tripled.
So, the correct answer is A. F/9.
To determine how the electric force will change when the distance between the charges is tripled, we can utilize Coulomb's Law, which governs the electric force between two point charges.
Coulomb's Law states that the electric force (F) between two point charges (q1 and q2) is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it is expressed as:
F = (k * q1 * q2) / r^2
Where:
F is the electric force
k is Coulomb's constant (a constant value determined experimentally)
q1 and q2 are the charges of the two point charges
r is the distance between the charges
Now, let's analyze the scenario given.
The electric force between the charges is initially F when the distance between them is r. We want to determine what the force will become if the distance is tripled.
Let's call the new distance between the charges "3r". Substituting this into Coulomb's Law, we get:
F' = (k * q1 * q2) / (3r)^2
Simplifying further:
F' = (k * q1 * q2) / 9r^2
As we can see, the electric force (F') is nine times smaller than the original force F because the denominator, 9r^2, is nine times larger than r^2.
Therefore, if the distance between the charges is tripled, the electric force will become F/9.
So, the correct answer is: A. F/9
since F = q1*q2 / r^2
if r changes to 3r, the force goes down to 1/9 as much
(3r)^2 = 9r^2