An alternating current I(t) = I0cos(ωt) flows through a circular wire loop of radius R, lying in the xy-plane, and centred at the origin. The electric field \(\vec{E}\) (\(\vec{r}\), t) and the magnetic field \(\vec{B}\)(\(\vec{r}\), t) are measured at a point \(\vec{r}\) such that r >> \(\frac{{\rm{c}}}{{\rm{\omega }}}\) >> R, where \(\vec{r}\) = \(\left| {\overrightarrow {\rm{r}} } \right|\). Which one of the following statements is correct?
1
The time-averaged \(\left| {\overrightarrow {{\rm{E}}\,} \,\left( {\overrightarrow {\rm{r}} ,{\rm{t}}} \right)} \right| \propto \frac{1}{{{r^2}}}\)
2
The time-averaged \(\left| {\overrightarrow {{\rm{E}}\,} \,\left( {\overrightarrow {\rm{r}} ,{\rm{t}}} \right)} \right| \propto \,{{\rm{\omega }}^2}\)
3
The time-averaged \({\overrightarrow {\rm{B}} \,\left( {\overrightarrow {\rm{r}} ,{\rm{t}}} \right)}\) as a function of the polar angle θ has a minimum at θ = π/2
4
\({\overrightarrow {\rm{B}} \,\left( {\overrightarrow {\rm{r}} ,{\rm{t}}} \right)}\) is along the azimuthal direction