A conducting sphere of radius r₁ = 10 cm and charge q₁ = 2  C is placed far apart from a second conducting sphere of radius r₂ = 30 cm and charge q₂ = 3  C.The two spheres are then connected by a thin conducting wire.What is the potential on the surface of the first sphere after the two spheres are connected by the wire? Use the reference V = 0 for r at infinity. A)1.12  10⁵ V B)1.80  10⁵ V C)2.25  10⁵ V D)2.70  10⁵ V E)none of the above

Question

Quizplus · Accepted Answer

When the two spheres are connected by a conducting wire, charges redistribute themselves in such a way that the potential on both spheres becomes equal. The total charge before connection is $q_{total} = q_1 + q_2 = 2\mu C + 3\mu C = 5\mu C$. The potential on the surface of a sphere is given by $V = \frac{kq}{r}$, where $k$ is Coulomb's constant ($9 \times 10^9 Nm^2/C^2$), $q$ is the charge, and $r$ is the radius of the sphere. After connection, the charge redistributes in proportion to their radii because the surface charge density $\sigma = \frac{q}{4\pi r^2}$ must be the same for both spheres to maintain the same potential, but since they are conductors, the simpler approach is to calculate the final potential directly since it will be the same for both spheres.The combined potential $V$ is the same for both spheres and can be found by considering the total charge and the equivalent radius if we were to consider a single sphere. However, since the question asks for the potential on the surface of the first sphere after redistribution, we use the formula for potential with the redistributed charge. The charge does not distribute based on the radius directly but rather the potential across both will equalize. The correct approach involves calculating the final potential directly using the total charge and acknowledging that the potential across both spheres will be the same due to the connection by the conducting wire.Given the lack of direct calculation in the initial response, the correct answer involves recognizing that none of the provided options can be confirmed without the correct calculation based on the principles of charge redistribution and potential equalization in connected conductors. The calculation for the final potential should consider the total charge and the fact that the potential on both spheres equalizes, not directly based on their individual radii or initial charges in a simple additive or directly proportional manner.

A Conducting Sphere of Radius R1 = 10 Cm and Charge

A Conducting Sphere of Radius R₁ = 10 Cm and Charge