Two charged particles are 8.5cm apart .They moved and the force on each of them is found to be tripled .How far apart are they now
F = constant / d^2
3 F = constant /x^2
F = c/(8.5^2)
3 F = 3c/(8.5^2) = c/x^2
3 x^2 = 8.5^2
x = 8.5/sqrt(3)
electric field strength follows the inverse square law
f d^2 = (3f) D^2
D^2 = d^2 / 3
D = 8.5 / √3
To solve this problem, we can use Coulomb's Law, which 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. Let's break down the steps to find the new distance:
1. Start by assuming the initial force as F1 and the initial distance as d1.
2. According to the problem, the force on each particle is tripled. So, the new force is F2 = 3 * F1.
3. Use Coulomb's Law to set up the equation for the force:
F = k * (q1 * q2) / (d^2)
Where F is the force, k is Coulomb's constant, q1 and q2 are the charges of the particles, and d is the distance between them.
Here, we can ignore the constant k since it remains the same throughout.
Therefore, F1 = (q1 * q2) / (d1^2) and F2 = (q1 * q2) / (d2^2), where d2 is the new distance.
4. Since the force is directly proportional to F = (q1 * q2) / (d^2), we can write:
F2 / F1 = (q1 * q2) / (d2^2) / (q1 * q2) / (d1^2)
3 = (d1^2) / (d2^2)
5. Rearrange the equation to isolate d2:
3 = (d1 / d2)^2
Taking the square root of both sides:
√3 = d1 / d2
6. Solve for d2:
d2 = d1 / √3
Substitute the given distance d1 as 8.5 cm:
d2 = 8.5 cm / √3
Simplifying the expression, we get:
d2 ≈ 4.91 cm
Therefore, the two charged particles are now approximately 4.91 cm apart.