Question

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.

Answer 1

18 V

Step-by-step explanation:

Let

r = Radius of pollen grain =
`6* 10^(-6)\ m` (general value)

E = Electric field =
`3* 10^6\ N/C`

Electric field is given by

`E=(kq)/(r^2)`

Voltage is given by

`V=(kq)/(r)`

`(V)/(E)=r\\\Rightarrow V=Er\\\Rightarrow V=3* 10^6* 6* 10^(-6)\\\Rightarrow V=18\ V`

The maximum voltage is 18 V