two small, identical conducting spheres A and B are a distance R apart; each carries the same charge Q. (a) What is the force sphere B exerts on sphere A? (b) An identical sphere with zero charge, sphere C, makes contact with sphere B and is then moved very far away. what is the net force now acting on sphere A? (c) Sphere C is brought back and now makes contact with sphere A and is then moved far away. What is the force on sphere A in this third case?
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(a) The force sphere B exerts on sphere A can be calculated using Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges (Q × Q) and inversely proportional to the square of the distance (1/R^2) between them. Therefore, the force (F) can be given as F = k(Q × Q)/R^2, where k is the electrostatic constant.
(b) After sphere C makes contact with sphere B and is moved far away, the net force acting on sphere A will be zero. This is because the charge on sphere B gets distributed over both sphere B and sphere C when they come in contact. Since sphere C is moved very far away, it will have negligible effect on sphere A, resulting in no force on sphere A.
(c) When sphere C is brought back and makes contact with sphere A and is then moved far away, the force on sphere A will again be zero. This is because, similar to the previous case, the charge on sphere C gets distributed over both sphere A and sphere C. Since sphere C is moved far away, it will have negligible effect on sphere A, resulting in no force on sphere A.
To answer these questions, we need to consider Coulomb's law, which relates the force between two charged objects to their charges and the distance between them. Coulomb's law states that 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.
Here's how we can approach each part of the question:
(a) To find the force sphere B exerts on sphere A, we can use Coulomb's law. The formula to calculate the force is given by:
F = (k * |Q1 * Q2|) / r^2
Where:
F is the force between the two spheres,
k is the electrostatic constant (k = 9 x 10^9 N m^2/C^2),
Q1 and Q2 are the charges of spheres A and B, respectively,
r is the distance between the centers of the spheres.
Since the spheres are identical, Q1 = Q2 = Q, and the distance between them is R, the formula simplifies to:
F = (k * |Q^2|) / R^2
(b) When the identical sphere C with zero charge makes contact with sphere B and is then moved very far away, the net force acting on sphere A changes. When sphere C comes in contact with sphere B, some charge will redistribute between them. However, since sphere C is moved very far away, the influence of its charge on sphere A becomes negligible. Thus, the net force on sphere A will remain the same as it was before sphere C made contact with sphere B.
Therefore, the net force on sphere A remains unchanged.
(c) In the third case, when sphere C makes contact with sphere A and is then moved far away, the net force acting on sphere A will change. When sphere C comes in contact with sphere A, some charge will redistribute between them. As a result, the charges on sphere A and sphere C will be equal and opposite.
Since sphere C is moved far away, its influence on sphere A becomes negligible. So, the net force acting on sphere A will be the same as the force due to the charge Q on sphere B alone, as calculated in part (a).
Therefore, the force on sphere A in this third case will be the same as the force calculated in part (a):
F = (k * |Q^2|) / R^2
Keep in mind that the direction of the force will depend on the sign of the charges (+/-) and the distance between the spheres.
(a) k Q^2/R^2 repulsive
(b) now Q on A and Q/2 on B (also Q/2 on C)
so k Q^2/2R^2
(c)1.5/2 = .75 Q on A and still Q/2 on B
k*.75 *.5 Q^2 /R^2 = .375 k Q^2/R^2