Answer:
The magnetic field is [tex]B = 8.20 *10^{-3} \ T[/tex]
Explanation:
From the question we are told that
The mass of the metal rod is [tex]m = 0.12 \ kg[/tex]
The current on the rod is [tex]I = 4.1 \ A[/tex]
The distance of separation(equivalent to length of the rod ) is [tex]L = 6.3 \ m[/tex]
The coefficient of kinetic friction is [tex]\mu_k = 0.18[/tex]
The kinetic frictional force is [tex]F_k = 0.212 \ N[/tex]
The constant speed is [tex]v = 5.1 \ m/s[/tex]
Generally the magnetic force on the rod is mathematically represented as
[tex]F = B * I * L[/tex]
For the rod to move with a constant velocity the magnetic force must be equal to the kinetic frictional force so
[tex]F_ k = B* I * L[/tex]
=> [tex]B = \frac{F_k}{L * I }[/tex]
=> [tex]B = \frac{0.212}{ 6.3 * 4.1 }[/tex]
=> [tex]B = 8.20 *10^{-3} \ T[/tex]
