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Breaking a Capacitor into Combinations

61.Two metal ...

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61.Two metal spheres of radii and B are connected by a thin wire their separation is very large compared to there are dimensions the capacitance of this system is

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Q. Two metal spheres of radii

a

b

are connected by a thin wire. Their separation is very large compared to their dimensions. The capacitance of this system is

Q. Two metal spheres (radii

r_{1}, r_{2}

r_{1} < r_{2}

) are very far apart but are connected by a thin wire. If their combined charge is Q, then what is their common potential?

Q. Two spheres have radii a and b and their centres are at a distance d apart. Show that the capacitance of this system is;

C = \frac{4 π ε_{o}}{\frac{1}{a} + \frac{1}{b} \pm \frac{2}{d}}

provided that d is large compared with a and b.

Q. Two conducting spheres of radii R₁ and R₂ are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series−parallel connections.

Q. Two spheres have radii a and b and their centres are at a distance d apart. The capacitance of this system is;

C = \frac{4 π ε_{o}}{\frac{1}{a} + \frac{1}{b} \pm \frac{2}{d}}

provided that d is large compared with

a

b

.

Show that as

d

approaches infinity the above result reduces to that of two isolated spheres in series.

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