Respuesta :
Answer: she will have to increase the factor of current by 11
Explanation: The mathematical relationship between the strength of the magnetic field (B) created by a current carrying conductor with current (I) is given by the Bio-Savart law given below
B=[tex]\frac{u_{0}I }{2\pi r}[/tex]
B=strength of magnetic field
I = current on conductor
r = distance on any point of the conductor from it center
u[tex]_{0}[/tex] = permeability of magnetic field in space
from the question, the investigator is trying to keep a constant magnetic field meaning B has a fixed value such as the constants in the formulae, the only variables here are current (I) and distance (r). We can get this a mathematical function.
by cross multipying, we have
B* 2πr=[tex]u_{0}[/tex]I
by dividing through to make I subject of formulae, we have that
I = [tex]\frac{B*2\pi r}{u_{0} }[/tex]
B, 2π and [tex]u_{0}[/tex] are all constants, thus
[tex]\frac{B*2\pi r}{u_{0} }[/tex] = k(constant)
thus we have that
I =kr (current is proportional to distance assuming magnetic field strength and other parameters are constant)
thus we have that
[tex]\frac{I_{1} }{r_{1} }[/tex]=[tex]\frac{I_{2} }{r_{2} }[/tex]
[tex]r_{1}[/tex]=1cm and [tex]r_{2}[/tex]=11cm
[tex]\frac{1_{1} }{1}[/tex]=[tex]\frac{I_{2} }{11}[/tex]
thus [tex]I_{2}[/tex]=11* [tex]I_{1}[/tex]
which means the second current is 11 times the first current
