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One insulated metal sphere is charged to a potential of 3xx10^(5) Volts. What should be the radius of the sphere so that it may cause breakdown in air? Dielectric strength of air is 3xx10^(6)V//m. |
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Answer» Solution :Electric FIELD intensity and electric potential at the surface of the metallic sphere of radius r and charge Q can be written as follows: `E=(1)/(4pi epsilon_(0)) *(q)/(r^(2)) "" …(i)` `V=(1)/(4pi epsilon_(0)) *(q)/(r )""...(ii)` So DIVIDING (i) by (ii), we get `(E )/(V)=(1)/(r ) rArr r=(V)/(E ) ""...(iii)` For BREAKDOWN in air, electric field intensity at the surface must be equal to dielectric STRENGTH of the air. `therefore E =` Dielectric strength `=3xx10^(6)V//m` Given, `V=3xx10^(5)V` `therefore` From (iii), `r=(3xx10^(5))/(3xx10^(6))=0.1m` |
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