two isolated conducting spheres of different radius and different charges are first brought in contact and then separated what happens to the final charge on each of the sphere
Well, let's see. When the two spheres are brought in contact, they have a nice little "charge-sharing party." They exchange some of their charges with each other, kind of like a game of "pass the charge." Now, if the spheres have different sizes and charges, it's like having a small clown and a big clown swapping their colorful balls. After they separate, the big clown might end up with more balls, while the small clown has fewer balls, meaning their final charges will be different. So, in short, the final charge on each sphere will depend on their initial charges and sizes. It's like a clown size and charge lottery!
When two conducting spheres are brought into contact and then separated, the charges on each sphere will redistribute to reach a new equilibrium.
Let's assume that sphere A has a larger radius and a charge of +Q, while sphere B has a smaller radius and a charge of +q.
Step 1: Contact
When the two spheres are brought into contact, electrons will flow from the sphere with higher negative charges to the sphere with fewer negative charges. This transfer of electrons equalizes the charge distribution.
Step 2: Separation
After the contact, when the spheres are separated, the charge distribution on each sphere will depend on their relative sizes and the charges they initially had.
Sphere A:
- The larger sphere (A) will acquire some negative charge (-q) from sphere B when they come into contact. This negative charge will distribute evenly on both spheres.
- After separation, sphere A will have a new charge of +(Q - q). This is because it had an initial charge of +Q and acquired a negative charge of -q during contact.
Sphere B:
- The smaller sphere (B) will lose some negative charge (-q) to sphere A when they come into contact. This negative charge will distribute evenly on both spheres.
- After separation, sphere B will have a new charge of +(q - q), which simplifies to zero. Sphere B will be left neutral since it completely transferred its charge to sphere A during contact.
In summary, sphere A will have a new charge of +(Q - q), while sphere B will have a charge of zero (neutral) after they are separated.
When two isolated conducting spheres of different radius and different charges are brought in contact and then separated, the final charge on each sphere depends on the initial charges and the ratio of their radii.
Let's denote the initial charges as Q1 and Q2, and the radii as r1 and r2, where Q1 and Q2 are the charges on spheres 1 and 2 respectively, and r1 and r2 are their radii.
When the spheres are brought in contact, the charges are distributed across both spheres due to the conductivity of the material. This redistribution happens in a way that the charges try to distribute evenly across the combined surface of both spheres.
To determine the final charge on each sphere, we need to consider the conservation of charge. The total charge before and after the contact remains the same.
So, the initial total charge is Q1 + Q2, and the final total charge will also be Q1 + Q2.
After separation, the charges on the spheres can be calculated using the concept of charge conservation. The charge will redistribute based on the ratios of their radii.
The ratio of the final charges can be determined using the equation:
Q1 / Q2 = (r2 / r1)^2
Thus, the final charge on sphere 1 (Q1) can be calculated by multiplying the initial total charge (Q1 + Q2) by (r2 / (r1 + r2))^2, and the final charge on sphere 2 (Q2) can be calculated by multiplying the initial total charge (Q1 + Q2) by (r1 / (r1 + r2))^2.
It is important to note that if the charges on the spheres have the opposite sign, their magnitudes would sum up to a new net charge after separation.
So, by using the above equation and understanding the concept of charge conservation, you can calculate the final charge on each of the spheres after they are brought in contact and then separated.