Answer:
0.4344A
Explanation:
From Ampere's law, it can be shown that the magnetic field B inside a long solenoid is
[tex]B= \mu_0NI[/tex]
Where
B= Magnetic field strenght at distance d
I= current
[tex]\mu_0 =[/tex]Permeability of free space ([tex]4\pi*10^{-7} Tm/A[/tex])
N= Number of loops
Our values are defined as follow,
[tex]N=10000[/tex]
[tex]B=5.25*10^{-5}[/tex]T
[tex]B'=5.25*10^{-5} * 104 = 5.46*10^{-3}T[/tex]
As a current required to become 104 times the Earth's magnetic field is required, we use B '
[tex]B'= \mu_0NI[/tex]
[tex]5.46*10^{-3}=4\pi*10^{-7}*10000*I[/tex]
[tex]I=\frac{5.46*10^{-3}}{4\pi*10^{-7}*10000}[/tex]
[tex]I=0.4344A[/tex]
Therefore is needed 0.4344A in the solenoid to produce a magnetic field inside the solenoid, near its center, that is 104 times the Earth's magnetic field.
