Conducting Objects Having Sharp Points Assignment Help | Conducting Objects Having Sharp Points Homework Help

Conducting Objects Having Sharp Points

Consider two conducting spheres of radii R1 and R2, placed in contact of each other. When a charge is given to this system, it rises to a common potential V. If q1 and q2 be the charges on the two spheres respectively, then we have

    V = 1/4πε0 q1/R1 = 1/1/4πε0 q2/R2
. :     q1/q2 = R1/R2

If σ1 and σ2 be the charge densities of the two spheres, we have
        σ1 = q1/4πR12 and σ2 = q2/4πR22
    . :    σ1/ σ2 = R1/R2                                    … (1)

Substituting the value of q1/q2 from Eq. (1), we get
        σ1/ σ2 = R2/R1
or        σ∞ 1/R
That is, smaller the radius of the sphere, higher is the charge density.
Thus if a conducting object has sharp points on its surface, the charge densities and hence the electric intensities near these points will be very high. These points will strongly attract the oppositely-charged ions of the surrounding air. These ions will therefore be accelerated and produce more ions by colliding with the air molecules. The air will thus become quite conducting giving rise to corona discharge. The air surrounding sharp conducting points may even glow by the light emitted from the air molecules during the collisions.

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