A coil consists of `200` turns of wire having a total reistance of `2.0Omega`. Each turn is a square of side `18cm,` and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from `0` to `0.5T` in `0.80s`, what is the magnitude of induced emf and current in the coil while the field is changing?

Options

A. 5.25 V
B. 3.2 V
C. 6.5 V
D. 4.05 V

Answer

D

Explanation

Given, number of turns, N=200 turns
side of square, `d=18cm=18xx10^(-2)m`
area of square, `S=d^(2)=(18xx10^-2)^(2)m^(2)`
change in field, `DeltaB=B_(2)-B_(a)=(0.5-0)T=0.5T`
induced emf, `|e|=`?
from the faraday's second law,
induced emf `|e|=(Nd phi)/(dt)=(N*S)(DeltaB)/(Deltat)=((200)(18xx10^(-2))^(2)0.5)/(0.8)=4.05`V