Answer :
1. 0.66 s
The current induced in the loop is
I = 0.20 A
while the resistance of the loop is
[tex]R=0.032 \Omega[/tex]
so the emf induced in the loop can be found by using Ohm's law
[tex]\epsilon = RI=(0.032 \Omega)(0.20 A)=0.0064 V[/tex]
We also know that according to Faraday-Newmann-Lenz, the induced emf is
[tex]\epsilon=-\frac{\Delta \Phi}{\Delta t}[/tex] (1)
where
[tex]\Delta \Phi[/tex] is the variation of magnetic flux through the loop
[tex]\Delta t[/tex] is the time interval
We have:
- Initial magnetic field: B = 1.5 T
- Radius of the coil: r = 30 mm = 0.03 m
- So, area of the coil: [tex]A=\pi r^2 = \pi (0.03 m)^2=2.83\cdot 10^{-3} m^2[/tex]
so the initial flux through the coil is
[tex]\Phi_i = B_i A = (1.5 T)(2.83\cdot 10^{-3}m^2)=4.25\cdot 10^{-3} Wb[/tex]
While the final flux through the coil is zero, since the magnetic field at the end is zero, so the change in magnetic flux is
[tex]\Delta \Phi = \Phi_f - \Phi_i = 0-4.25\cdot 10^{-3} Wb=-4.25\cdot 10^{-3} Wb[/tex]
Now re-arranging eq.(1) we find the time interval needed:
[tex]\Delta t = -\frac{\Delta \Phi}{\epsilon}=-\frac{-4.25\cdot 10^{-3} Wb}{0.0064 V}=0.66 s[/tex]
2. Same direction as the external magnetic field
The direction of the induced magnetic field is given by Lenz's law.
In fact, Lenz law states that the induced current in the loop is such that the magnetic field opposes the variation of magnetic flux through the coil.
Here, the magnetic flux through the coil is decreasing, since the external magnetic field is decreasing: this means that the induced magnetic field must be in the same direction as the external magnetic field (in order to restore the flux and to oppose this decrease of flux).
The amount of time it would take for the magnitude of the uniform magnetic field to drop is 0.66 seconds.
Given the following data:
Radius = 30 mm to meters = 0.02 m.
Resistance = 0.032 Ω.
Magnetic field = 1.5 T.
Current = 0.20 A.
How to calculate the time.
In order to determine the amount of time it would take for the magnitude of the uniform magnetic field to drop from 1.5 Tesla to zero (0), we would apply Faraday-Newmann-Lenz equation.
For the wire's area:
[tex]A = \pi r^2\\\\A= 3.142 \times 0.03^2\\\\A=2.83 \times 10^{-3}\;m^2[/tex]
For the initial magnetic flux:
[tex]\phi _i = B_i A\\\\\phi _i = 1.5 \times 2.83 \times 10^{-3}\\\\\phi _i = 4.25 \times 10^{-3}\;Wb[/tex]
For the change in magnetic flux:
[tex]\Delta \phi = \phi_f - \phi_i\\\\\Delta \phi =0-4.25\times 10^{-3}\\\\\Delta \phi =-4.25\times 10^{-3}\;Wb[/tex]
From Faraday-Newmann-Lenz equation, we have:
[tex]\epsilon =-\frac{\Delta \phi}{\Delta t} \\\\\Delta t=-\frac{\Delta \phi}{\epsilon} \\\\\Delta t=-(\frac{-4.25\times 10^{-3}}{0.20 \times 0.032})\\\\\Delta t=\frac{4.25\times 10^{-3}}{0.0064}\\\\\Delta t=0.66\;seconds[/tex]
The direction of the induced magnetic field that is caused by this current is in the same direction as the external magnetic field in accordance with Lenz's law.
Read more on magnetic field here: https://brainly.com/question/7802337