A coil is wrapped with 332 turns of wire on the perimeter of a circular frame (of radius 30 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is directed perpendicular to the plane of the coil. This field changes at a constant rate from 29 mT to 56 mT in 63 ms. What is the magnitude of the induced average E in the coil, over the time interval 63 ms during which the field changes

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okpalawalter8 okpalawalter8 · Answer 1 · 2021-06-24T04:15:17+02:00

Answer:

[tex]E=84.5V[/tex]

Explanation:

From the question we are told that:

Number of Turns [tex]N=332turns[/tex]

Radius [tex]r= 30cm[/tex]

Field Change [tex]B=56mt-29mt=27mt[/tex]

Time [tex]t=63ms[/tex]

Generally the equation for Magnetic Field is mathematically given by

[tex]\frac{dB}{dt}=\frac{27*10^{-3}}{29*10^{-3}}[/tex]

[tex]\frac{dB}{dt}=0.9T/s[/tex]

Generally the Flux at 332 turns is mathematically given by

[tex]\phi=N*A*B[/tex]

Generally the equation for Area of coil is mathematically given by

[tex]A=\pi*r^2[/tex]

[tex]A=\pi*(r*10^{-2})^2[/tex]

Since

[tex]\phi=332*\pi*(\theta*10^{-2})^2*B[/tex]

Therefore

[tex]\frac{d \phi}{dt}=332*\pi*(900*10^{-4}*\frac{dB}{dt}[/tex]

Generally the equation for emf Magnitude is mathematically given by

[tex]E=\frac{d\phi}{dt}[/tex]

[tex]E=332*\pi*(900*10^{-4}*0.9[/tex]

[tex]E=84.5V[/tex]