Question

A straight Beam of ultrarelavistic electrons confined within a very long cylindrical region of radius less than 1 mm carries a current of 0.01 uA. The strength of the electric field at a point 2cm away from the beam axis will be nearest to

Answer 1

As per the given question,

The radius of the cylindrical wire $(r)<1mm$

Current flowing in the wire $(I)=0.01 \mu A$

Electric field at a distance d=2cm from the wire =?

$B=\frac{\mu_o i}{2\pi r}$

But, $E=\frac{dB}{dt}$

So, $E=\frac{d}{dt}(\frac{\mu i}{2\pi r})$

$E=\frac{2\times 10^{-7}\times 0.01\times 10^{-6}}{2\times 10^{-2}}N/c$

$E=1\times 10^{-13} N/c$