Answer:
[tex]3.81972\times 10^{-7}\ A[/tex]
Explanation:
B = Magnetic field = [tex]3\times 10^{-8}\ G[/tex]
d = Diameter of loop = 16 cm
r = Radius = [tex]\frac{d}{2}=\frac{16}{2}=8\ cm[/tex]
i = Current
[tex]\mu_0[/tex] = Vacuum permeability = [tex]4\pi \times 10^{-7}\ H/m[/tex]
The magnetic field of a loop is given by
[tex]B=\frac{\mu_0i}{2r}\\\Rightarrow i=\frac{B2r}{\mu_0}\\\Rightarrow i=\frac{3\times 10^{-8}\times 10^{-4}\times 2\times 0.08}{4\pi\times 10^{-7}}\\\Rightarrow i=3.81972\times 10^{-7}\ A[/tex]
The current needed to produce such a field at the center of the loop is [tex]3.81972\times 10^{-7}\ A[/tex]
