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Electricity and Magnetism

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Moderate

Potential of Two Attached Conducting Spheres

EANDM-AT08KZ

Two conducting spheres, $A$ and $B$, are initially isolated from one another. Sphere $A$ has a radius of $a$ and has an initial charge of $Q_A$. Sphere $B$ has a radius of $b$ with an initial charge of $Q_B$. The sphere's are subsequently attached by a thin conducting wire.

What is the charge $ Q^{new}_A$ on sphere $A$, after it is connected to to sphere $B$ (in terms of the radii of the two spheres and the initial charges on each)?

A

$Q^{new}_A = \cfrac{Q_A + Q_b}{\bigg(1 +\cfrac{a}{b}\bigg)}$

B

$Q^{new}_A = \cfrac{Q_A }{\bigg(\cfrac{b}{a}\bigg)}$

C

$Q^{new}_A = \cfrac{Q_A + Q_b}{2}$

D

$Q^{new}_A = \cfrac{Q_A + Q_b}{\bigg(1 +\cfrac{b}{a}\bigg)}$