Question

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

Answer 1

Answer:

$E=84.5V$

Explanation:

From the question we are told that:

Number of Turns $N=332turns$

Radius $r= 30cm$

Field Change $B=56mt-29mt=27mt$

Time $t=63ms$

Generally the equation for Magnetic Field is mathematically given by

 $\frac{dB}{dt}=\frac{27*10^{-3}}{29*10^{-3}}$

 $\frac{dB}{dt}=0.9T/s$

Generally the Flux at 332 turns is  mathematically given by

 $\phi=N*A*B$

Generally the equation for Area of coil is mathematically given by

 $A=\pi*r^2$

 $A=\pi*(r*10^{-2})^2$

Since

 $\phi=332*\pi*(\theta*10^{-2})^2*B$

Therefore

 $\frac{d \phi}{dt}=332*\pi*(900*10^{-4}*\frac{dB}{dt}$

Generally the equation for emf Magnitude is mathematically given by

 $E=\frac{d\phi}{dt}$

 $E=332*\pi*(900*10^{-4}*0.9$

 $E=84.5V$