Question:

Two spherical conductors, A and B, are initially uncharged.

a) Conductor A has a radius of 0.05 m and is positively charged with a charge of 2 μC.

b) Conductor B has a radius of 0.1 m and is negatively charged with a charge of -3 μC.

The conductors are brought into contact with each other and then separated.

a) Calculate the initial electric field at a distance of 0.1 m from conductor A.

b) Calculate the charge on conductor B after contact.

c) Determine the final electric field at a distance of 0.1 m from conductor A after the separation.

Given:

• ε₀ (vacuum permittivity) = 8.854 x 10⁻¹² C²/N·m²

• Coulomb's constant k = 8.99 x 10⁹ N·m²/C²

Answer:

a) To calculate the initial electric field at a distance of 0.1 m from conductor A, we can use the formula for the electric field E due to a point charge:

E = k * (q / r²)

where E is the electric field, k is the Coulomb's constant, q is the charge, and r is the distance from the charge.

Plugging in the values:

E = (8.99 x 10⁹ N·m²/C²) * (2 x 10⁻⁶ C) / (0.1 m)²

E = 1.798 x 10⁷ N/C

Therefore, the initial electric field at a distance of 0.1 m from conductor A is 1.798 x 10⁷ N/C.

b) When conductors A and B are brought into contact, they will reach an equilibrium state where their charges redistribute. The final charge on conductor B can be calculated using conservation of charge.

The total charge before the contact = charge on A + charge on B

Total charge before = 2 x 10⁻⁶ C - 3 x 10⁻⁶ C = -1 x 10⁻⁶ C

Since the total charge remains conserved:

Total charge after = 0 C

Therefore, the charge on conductor B after contact is 1 x 10⁻⁶ C.

c) To determine the final electric field at a distance of 0.1 m from conductor A after separation, we can consider that after separation, charges will distribute uniformly on each conductor's surface. For conducting spheres, the electric field inside the spheres is zero.

Therefore, the final electric field at a distance of 0.1 m from conductor A after separation is zero.

Thus, the final electric field at a distance of 0.1 m from conductor A after separation is 0 N/C.