Answer:
The value is [tex]B = 0.2312 \ T[/tex]
The direction is into the surface
Explanation:
From the question we are told that
The mass density is [tex]\mu =\frac{m}{L} = 1.17 \ g/cm =0.117 kg/m[/tex]
The coefficient of kinetic friction is [tex]\mu_k = 0.250[/tex]
The current the wire carries is [tex]I = 1.24 \ A[/tex]
Generally the magnetic force acting on the wire is mathematically represented as
[tex]F_F = F_B[/tex]
Here [tex]F_F[/tex] is the frictional force which is mathematically represented as
[tex]F_F = \mu_k * m * g[/tex]
While [tex]F_B[/tex] is the magnetic force which is mathematically represented as
[tex]F_B = BILsin(\theta )[/tex]
Here [tex]\theta =90^o[/tex] is the angle between the direction of the force and that of the current
So
[tex]F_B = BIL[/tex]
So
[tex]BIL = \mu_k * m * g[/tex]
=> [tex]B = \mu_k * \frac{m}{L} * [\frac{g}{I} ][/tex]
=> [tex]B = 0.25 * 0.117 * [\frac{9.8}{1.24} ][/tex]
=> [tex]B = 0.2312 \ T[/tex]
Apply the right hand curling rule , the thumb pointing towards that direction of the current we see that the direction of the magnetic field is into the surface as shown on the first uploaded image
