Answer
$4.51\times10^{-22}\,T$
Work Step by Step
Given/Known: $\mu_{0}=4\pi\times10^{-7}\,T\cdot m/A,$ $\varepsilon_{0}=8.854\times10^{-12}\,F/m,$ $r=5.00\times10^{-2}\,m,$ $R=3.00\times10^{-2}\,m,$ $E=(4.50\times10^{-3}\,V/m\cdot s)t$
According to Maxwell's law of induction,
$\oint \vec{B}\cdot d\vec{s}=\mu_{0}\varepsilon_{0}\frac{d\Phi_{E}}{dt}=\mu_{0}\varepsilon_{0}\frac{d}{dt}(EA\cos0^{\circ})=\mu_{0}\varepsilon_{0}A\frac{dE}{dt}$
We need to find B at a radial distance $r=5.0\,cm$,But electric field is limited to the area of a circle with $R=3.00\,cm$.
$\implies B\times2\pi r=\mu_{0}\varepsilon_{0}\times\pi R^{2}\times\frac{dE}{dt}$
Or $B=\frac{\mu_{0}\varepsilon_{0}R^{2}}{2r}\times\frac{dE}{dt}$
Result: $B=$
$\frac{4\pi\times10^{-7}\,T\cdot m/A\times8.854\times10^{-12}\,F/m\times(3.00\times10^{-2}\,m)^{2}}{2\times5.00\times10^{-2}\,m}\times\frac{d}{dt}(4.50\times10^{-3}\,V/m\cdot s)t$
$=4.51\times10^{-22}\,T$
