two pint charges are 4 cm apart. They are moved to a new distance of 2 cm. By what factor does the resulting mutual forces between them change.
a. 1/2
b. 2
c. 1/4
d. 4
1/4
To determine the factor by which the resulting mutual forces between two pint charges change when they are moved to a new distance, we can use Coulomb's Law. Coulomb's Law states that the 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.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges
k is the electrostatic constant (k ≈ 9 x 10^9 N m^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
In this case, since the charges are the same, we can assume that q1 = q2 = q.
Initially, the distance between the charges is 4 cm = 0.04 m.
The initial force is:
F_initial = k * (q * q) / (0.04)^2
When the charges are moved to a new distance of 2 cm = 0.02 m, the force becomes:
F_final = k * (q * q) / (0.02)^2
To calculate the factor by which the resulting mutual forces change, we divide the final force by the initial force:
Factor = F_final / F_initial
Now, let's calculate the factor:
Factor = (k * (q * q) / (0.02)^2) / (k * (q * q) / (0.04)^2)
Factor = ((0.04)^2 / (0.02)^2) = (0.0016 / 0.0004) = 4
Therefore, the resulting mutual forces between the charges change by a factor of 4.
The answer is d. 4.
To determine the factor by which the resulting mutual forces between the two pint charges change when they are moved from a distance of 4 cm to a distance of 2 cm, we can use Coulomb's Law.
Coulomb's Law states that the 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 is expressed as:
F = k * (q1 * q2) / r^2
Where:
- F is the magnitude of the electrostatic force between the charges,
- k is Coulomb's constant (a constant value),
- q1 and q2 are the magnitudes of the charges, and
- r is the distance between the charges.
Let's call the initial force between the two charges F1 when they are 4 cm apart, and the resulting force F2 when they are 2 cm apart.
Since the charges remain the same, we can write the ratio of the forces as:
F2 / F1 = (k * (q1 * q2) / 2^2) / (k * (q1 * q2) / 4^2)
Simplifying this expression, we find:
F2 / F1 = (4^2 / 2^2)
F2 / F1 = 16 / 4
F2 / F1 = 4
Therefore, the resulting mutual forces between the two charges change by a factor of 4, which corresponds to option d.
So, the correct answer is d. 4