When two unequal point charges are released a distance d from one another, the heavier one has an acceleration a. If you want to reduce this acceleration to one-fifth of this value, how far (in terms of d) should the charges be when released?
F = k(q1q2)/r^2.
To reduce the force to 1/5 by changing distance, increase the distance by sqrt(5).
So the charges should be d*sqrt(5) apart.
so it should be 2.236 that is the sqrt(5)
or do i have to solve it by using that equation.. because i don't have q1 and q2
The distance in terms of d is d*sqrt(5). Whether you have to convert it to 2.236*d depends on your teacher.
With the information given, you are not expected to solve for an actual value. Just leave it in terms of d.
ok thank you
To solve this problem, we need to use the concept of Coulomb's law and the principle of superposition. Coulomb's law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Let's assume the charges are q1 and q2, and their masses are m1 and m2, respectively. The heavier charge will experience a greater force due to the attraction or repulsion between the charges.
Given that the heavier charge has an acceleration of a when released, we can equate the force experienced by the heavier charge to its mass multiplied by its acceleration:
F1 = m1 * a
Let's assume that initially, the charges are at a distance d from each other, and the heavier charge has a mass m1. When we want to reduce the acceleration to one-fifth of the original value, the new acceleration will be a/5.
Now, we can set up two equations using Coulomb's law to relate the forces and distances when the acceleration is a/5:
F1 = k * (q1 * q2) / (d^2)
F2 = k * (q1 * q2) / (x^2)
Where F1 and F2 are the forces experienced by the heavier charge when released at a distance d and x, respectively, k is the Coulomb's constant, q1 and q2 are the magnitudes of the charges, and x represents the new distance between the charges.
Since we want to reduce the acceleration, we can set up the following ratio:
F2 / F1 = (a/5) / a
From Coulomb's law, we know that F is inversely proportional to the square of the distance. So, we can write the ratio in terms of distances:
(x^2) / (d^2) = (1/5)
Now, we can solve for x in terms of d:
x^2 = (1/5) * (d^2)
x = sqrt((1/5) * (d^2))
Therefore, the charges should be released at a distance of sqrt((1/5) * (d^2)) in order to reduce the acceleration to one-fifth of its initial value.