Answer :
Answer:
[tex]r=\dfrac{R}{2}[/tex]
Explanation:
We know that maximum value of magnetic field in the long wire
[tex]B_{max}=\dfrac{\mu _oI}{2\pi R}[/tex]
I=Current ,R=Radius of wire ,B= magnetic field
μo=Constant
At distance r the magnetic filed is the half of the maximum magnetic filed
At distance r
[tex]B=\dfrac{\mu _oIr}{2\pi R^2}[/tex]
[tex]B=\dfrac{B_{max}}{2}[/tex]
So we can say that
[tex]\dfrac{\mu _oIr}{2\pi R^2}=\dfrac{1}{2}\times \dfrac{\mu _oI}{2\pi R}[/tex]
[tex]r=\dfrac{R}{2}[/tex]
Therefore the answer is [tex]r=\dfrac{R}{2}[/tex]