The strength of the magnetic field is ![4.8\cdot 10^{-5} T](https://tex.z-dn.net/?f=4.8%5Ccdot%2010%5E%7B-5%7D%20T)
Explanation:
According to Faraday's Law, the magnitude of the induced emf in the coil is equal to the rate of changeof the flux linkage through the coil:
(1)
where
N = 505 is the number of turns in the coil
is the change in magnetic flux through the coil
is the time interval
![\epsilon = 0.166 V](https://tex.z-dn.net/?f=%5Cepsilon%20%3D%200.166%20V)
The coil is rotated from a position perpendicular to the Earth's magnetic field to a position parallel to it, so the final flux is zero, and the magnitude of the flux change is simply equal to the initial flux:
![\Delta \Phi = B A cos \theta](https://tex.z-dn.net/?f=%5CDelta%20%5CPhi%20%3D%20B%20A%20cos%20%5Ctheta)
where
B is the strength of the magnetic field
A is the area of the coil
is the angle between the normal to the coil and the field
The area of the coil can be written as
![A=\pi r^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2)
where
is its radius
Substituting everything into eq.(1) and solving for B, we find:
![\epsilon= \frac{NB\pi r^2 cos \theta}{\Delta t}\\B=\frac{\epsilon \Delta t}{\pi r^2 cos \theta}=\frac{(0.166)(2.77\cdot 10^{-3})}{(505)\pi (7.75\cdot 10^{-2})^2(cos 0^{\circ})}=4.8\cdot 10^{-5} T](https://tex.z-dn.net/?f=%5Cepsilon%3D%20%5Cfrac%7BNB%5Cpi%20r%5E2%20cos%20%5Ctheta%7D%7B%5CDelta%20t%7D%5C%5CB%3D%5Cfrac%7B%5Cepsilon%20%5CDelta%20t%7D%7B%5Cpi%20r%5E2%20cos%20%5Ctheta%7D%3D%5Cfrac%7B%280.166%29%282.77%5Ccdot%2010%5E%7B-3%7D%29%7D%7B%28505%29%5Cpi%20%287.75%5Ccdot%2010%5E%7B-2%7D%29%5E2%28cos%200%5E%7B%5Ccirc%7D%29%7D%3D4.8%5Ccdot%2010%5E%7B-5%7D%20T)
Learn more about magnetic fields:
brainly.com/question/3874443
brainly.com/question/4240735
#LearnwithBrainly