Answer:
The value is [tex]F_{max} = 12 \muN [/tex]
Explanation:
From the question we are told that
The length is [tex]l = 2.0 \ cm = 0.02 \ m[/tex]
The radius of the the solenoid is [tex]r =40 \ cm[/tex]
The number of turns per meter is [tex]N = 800 \ turns / m[/tex]
The current through the solenoid is [tex]I = 50 \ mA = 50*10^{-3} \ A[/tex]
The current through the segment is [tex]I_s = 12 \ A[/tex]
Generally the magnetic force is mathematically represented as
[tex]F = B * I_s l sin(\theta)[/tex]
At maximum [tex]\theta = 90^o[/tex]
So
[tex]F_{max} = B * I_s l [/tex]
Here B is the magnetic field is mathematically represented as
[tex]B = \mu_o * N * I[/tex]
Here [tex]\mu_o[/tex] is the permeability of free space with value
[tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]
So
[tex]B = 4\pi * 10^{-7} * 800 *50*10^{-3} [/tex]
=> [tex]B = 5.0272 *10^{-5} \ T [/tex]
So
[tex]F_{max} = 5.0272 *10^{-5} * 12 * 0.02 [/tex]
[tex]F_{max} = 1.2 *10^{-5} [/tex]
[tex]F_{max} = 12 \muN [/tex]
