Answer:
a
The magnitude of magnetic field is [tex]B=7.18*10^{-6}T[/tex]
b
The torque is [tex]\tau= 6.12*10^{-8} Joules[/tex]
Explanation:
From the question we are told that
The radius of the circular loop is [tex]r = 14 \ cm = \frac{14}{100} = 0.14 m[/tex]
The current carried by the circular loop is [tex]I_l = 16A[/tex]
The radius of the flat loop is [tex]r_f = 0.68cm = \frac{0.68}{100} = 0.0068m[/tex]
The current carried by the flat loop [tex]I_f =1.4A[/tex]
The magnitude magnetic field produce at the center due to the circular loop is mathematically represented as
[tex]B = \frac{\mu_o I_i}{2 * r}[/tex]
Where [tex]\mu_0[/tex] is the permeability of free space with a value of [tex]\mu = 4 \pi *10^{-7} H/m[/tex]
Substituting values
[tex]B= \frac{4\pi *10^{-7} * 16}{2(1.4)}[/tex]
[tex]B=7.18*10^{-6}T[/tex]
The torque on the coil due to the loop is mathematically represented as
[tex]\tau = BIAN[/tex]
Where A is the area and it is evaluated as
[tex]A = \pi r^2[/tex]
[tex]=3.142 * 0.0068^2[/tex]
[tex]=0.000145m^2[/tex]
N is the number of turns with value N = 42 turns
No substituting values into the equation for torque
[tex]\tau = 7.18*10^{-6} * 1.4 * 0.000145 *42[/tex]
[tex]\tau= 6.12*10^{-8} Joules[/tex]
