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A pollen grain has a maximum electric charge it can carry before the electric field it generates exceeds the dielectric limit for air of 3 × 10 6 N / C . 3×106 N/C. Estimate the magnitude of the maximum voltage V max Vmax at the surface of a pollen grain that is carrying its maximum electric charge, assuming V = 0 V=0 at infinity.

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Answer:

18 V

Explanation:

Let

r = Radius of pollen grain = [tex]6\times 10^{-6}\ m[/tex] (general value)

E = Electric field = [tex]3\times 10^6\ N/C[/tex]

Electric field is given by

[tex]E=\dfrac{kq}{r^2}[/tex]

Voltage is given by

[tex]V=\dfrac{kq}{r}[/tex]

[tex]\dfrac{V}{E}=r\\\Rightarrow V=Er\\\Rightarrow V=3\times 10^6\times 6\times 10^{-6}\\\Rightarrow V=18\ V[/tex]

The maximum voltage is 18 V

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