How does the electric force between two charged particles change if the
distance between them is increased by a factor of 3?
A. It is increased by a factor of 3.
B. It is increased by a factor of 9.
C. It is reduced by a factor of 9.
D. It is reduced by a factor of 3.
C
F ∝ 1/d^2
When the distance between two charged particles is increased by a factor of 3, the electric force between them changes. To understand how the electric force changes, we can refer to Coulomb's law, which states that the electric force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, the equation for Coulomb's law is given as:
F = (k * q1 * q2) / r^2
Where:
F is the electric force between the particles,
k is the electrostatic constant,
q1 and q2 are the charges of the particles,
and r is the distance between the particles.
Now, if the distance between the charges is increased by a factor of 3, it means the new distance (r') is three times the original distance (r). Hence, r' = 3r.
Substituting r' into the Coulomb's law equation, we get:
F' = (k * q1 * q2) / (3r)^2
= (k * q1 * q2) / 9r^2
= F / 9
Therefore, when the distance between the charges is increased by a factor of 3, the electric force between them is reduced by a factor of 9. Hence, the correct answer is option C: It is reduced by a factor of 9.
The electric force between two charged particles is given by Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
When the distance between the particles is increased by a factor of 3, it means that the new distance is 3 times the initial distance.
According to Coulomb's law, if the distance between the particles is increased by a factor of 3, the electric force between them will be reduced by the square of that factor.
Therefore, the electric force will be reduced by a factor of 3^2 = 9.
So, the correct answer is C. It is reduced by a factor of 9.