Two similar sphere having charge -2C and +4C respectively are separated by distance "r" exert force (F=16N) third similar neutral sphere is first touched with sphere B and then sphere A. then force between spheres decreases by:
When the third neutral sphere is first touched with sphere B (+4C), the charges are shared equally between them, so each sphere has a charge of +2C. Then, when the neutral sphere (now charged with +2C) is touched with sphere A (-2C), the charges are again shared equally between them, and both spheres become neutral (0C).
Now, the force between the two spheres is given by Coulomb's Law:
F = k * (q1 * q2) / r^2
Where F is the force, k is Coulomb's constant, q1 and q2 are the charges on the two spheres, and r is the distance between them.
Initially, the force between the two spheres was 16 N, so:
16 = k * (-2C * +4C) / r^2
After touching the neutral sphere, both sphere A and sphere B become neutral, so the force between them will be 0, as they have no charge.
The decrease in force can be calculated as:
Decrease in force = Initial force - Final force
Decrease = 16 - 0
Decrease = 16 N
The force between two charged spheres is given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where F is the force, k is the electrostatic constant, q1 and q2 are the charges on the spheres, and r is the distance between the centers of the spheres.
In this case, we have two similar spheres with charges -2C and +4C respectively. Let's denote the force between these spheres as F1. So:
F1 = (k * |-2C * +4C|) / r^2
Given that F1 = 16N, we can solve for the value of k using this equation.
16N = (k * |-2C * +4C|) / r^2
Let's consider the second scenario when a third similar neutral sphere is first touched with sphere B and then sphere A.
When the spheres are touched, charges are transferred due to contact. Sphere B had a charge of +4C and sphere A had a charge of -2C. After contact, charge will redistribute between the spheres, but the total charge remains constant. Let's denote the charges on sphere B and A as qB and qA respectively after contact.
As sphere B is positively charged, it will transfer some positive charge to sphere A and acquire some negative charge from sphere A. Therefore, qB will decrease and qA will increase.
Let's assume that after contact, qB and qA are the charges on spheres B and A respectively. The total charge remains the same, so:
qB + qA = -2C + 4C (charge on sphere A after contact) = 2C
Now, let's calculate the force between the spheres after contact, denoted as F2:
F2 = (k * |qB * qA|) / r^2
From the given information, we know that the force between the spheres decreases. So, we need to find the difference between F1 and F2:
ΔF = F2 - F1
Substituting the values of F1 and F2 into the equation:
ΔF = [(k * |qB * qA|) / r^2] - [(k * |-2C * +4C|) / r^2]
Now, we need to find the values of qB and qA after contact. This depends on the specific conditions of the contact, such as conductivity of the spheres and the way the contact is made. Without more information, it is not possible to determine the exact values of qB and qA after contact, and consequently, the exact change in force between the spheres.
Therefore, we cannot determine the specific decrease in force between the spheres without additional information.
To find the change in force between the two spheres, we need to understand the concept of Coulomb's law and how charges interact with each other.
According to Coulomb's law, the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It can be mathematically represented as:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the two charges,
k is the electrostatic constant (~ 9 * 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the charges on sphere A and B, and
r is the distance between the centers of the spheres.
Let's calculate the initial force between sphere A and B using the given information.
Given:
Charge on sphere A (q1) = -2C
Charge on sphere B (q2) = +4C
Force between A and B (F_initial) = 16N
F_initial = (k * |q1 * q2|) / r^2
16 = (9 * 10^9 * |(-2) * 4|) / r^2
16 = (9 * 10^9 * 8) / r^2
r^2 = (9 * 10^9 * 8) / 16
r^2 = 4.5 * 10^9
r = sqrt(4.5 * 10^9)
r ≈ 67,082 meters
Now, let's consider the third neutral sphere that is first touched with sphere B and then with sphere A. When two spheres come into contact, they share their charges to equalize the potential.
Since sphere B has a charge of +4C and the third sphere is neutral, the third sphere acquires a charge of +4C. Now, when the third sphere is touched with sphere A, which has a charge of -2C, they will also share their charges.
The charges transfer from sphere B to the third sphere, resulting in both of them having a charge of +2C. The sphere A remains with a charge of -2C.
Now, let's calculate the new force between spheres A and B.
New force between A and B (F_new) = (k * |q1 * q2|) / r^2
F_new = (9 * 10^9 * |(-2) * 2|) / (67,082^2)
F_new = (9 * 10^9 * 4) / (67,082^2)
F_new ≈ 3N
Therefore, the force between the spheres decreases from 16N to approximately 3N after the charges are shared between the spheres.