The electric field at a point on the axial line at a distance of 10 cm from the centre of an electrc dipole is `3.75xx10^(5)` N/C in air, while at a distance of 20 cm, the electric field is `3xx10^(4)` N/C. Calculate the length of an electric dipole.

Explanation

We know that,
`E_("axial")=(2pr)/((r^(2)-a^(2))^(2))`
Case I When `r=10" cm"=0.1m`
`E_("axial")=3.75xx10^(5)" N/C"`
`3.75xx10^(5)=9xx10^(9)xx(2pxx0.1)/([(0.1)^(2)-a^(2)]^(2))` . . . . (i)
Case II When `r=20" cm"=0.2m`
`E_("axial")=3xx10^(4)" N/C"`
`3xx10^(4)=9xx10^(9)xx(2pxx0.2)/([(0.2)^(2)-a^(2)]^(2))`
On solving Eqs. (i) and (ii), we get
`a=0.05` m
Therefore, length of the dipole is 2a.
So, `2a=2xx0.05`
or `2a=0.1` m