Question

Two metal spheres of radii a and b are connected by a thin wire. Their separation is very large compared to their dimensions. The capacitance of this system is

Answer 1

•TWO METAL SPHERES OF RADII a and b ARE CONNECTED BY A THIN WIRE. THEIR SEPARATION IS VERY LARGE COMPARED TO THEIR DIMENSIONS.THEN THE CAPACITANCE OF THE SYSTEM WOULD BE 4π£(a+b).

• The CAPACITANCE OF BOTH THE SPHERES ARE 4π£a and 4π£b respectively.

• When a THIN WIRE is used to CONNECT BOTH THE METAL SPHERES, THE CAPACITANCE OF THE SYSTEM would be

Ceq= Ca+ Cb

= 4π£(a+b)

Answer 2

The capacitance of this system = 4$\pi$$\mathcal{E}_o$ (a+b)

Given:

Two metal spheres of radii a and b are connected by a thin wire.

Their separation is very large compared to their dimensions.

To find:

The capacitance of this system.

Formula used:

Capacitance = $\mathcal{E}_o$$\frac{A}{d}$

Explanation:

Here Their separation is very large compared to their dimensions so it can be neglected.

So     $C_{eq}$ = $C_1$ + $C_2$

Capacitance of sphere = 4$\pi$$\mathcal{E}_o$r

Spheres of radii a and b

So that   $C_{eq}$ = $C_1$ + $C_2$

              $C_{eq}$ = 4$\pi$$\mathcal{E}_o$a + 4$\pi$$\mathcal{E}_o$b

              $C_{eq}$  = 4$\pi$$\mathcal{E}_o$ (a+b)

The capacitance of this system = 4$\pi$$\mathcal{E}_o$ (a+b)

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