Question 229: Electromagnetic Induction

Question

The magnetic flux through a coil is $4 	imes 10^{-4} \mathrm{~Wb}$ at time $t=0$. It reduces to $30 \%$ of its original value in time $t$ second. If e.m.f. induced in the coil is 0.56 mV then the value of $t$ is

Accepted Answer

Given:
Initial flux, $\phi_1 = 4 	imes 10^{-4}~	ext{Wb}$
Final flux, $\phi_2 = 30\%$ of $\phi_1 = 0.3 	imes 4 	imes 10^{-4} = 1.2 	imes 10^{-4}~	ext{Wb}$
Induced emf, $e = 0.56~	ext{mV} = 0.56 	imes 10^{-3}~	ext{V}$
Time interval, $t = ?$
Step 1: Formula for average induced emf
$ e = \frac{\left|\phi_2 - \phi_1ight|}{t} $
Step 2: Substituting the values
$ e = \frac{\left|1.2 	imes 10^{-4} - 4 	imes 10^{-4}ight|}{t} $
$ e = \frac{\left|-2.8 	imes 10^{-4}ight|}{t} $
$ e = \frac{2.8 	imes 10^{-4}}{t} $
Given $e = 0.56 	imes 10^{-3}~	ext{V} = 5.6 	imes 10^{-4}~	ext{V}$ (But $0.56~	ext{mV}$ is $0.56 	imes 10^{-3}$, or $5.6 	imes 10^{-4}$ Ã¢ÂÂ check carefully.)
But $0.56~	ext{mV} = 0.56 	imes 10^{-3} = 5.6 	imes 10^{-4}~	ext{V}$
So,
$ 5.6 	imes 10^{-4} = \frac{2.8 	imes 10^{-4}}{t} $
Step 3: Solve for $t$
$ 5.6 	imes 10^{-4} \cdot t = 2.8 	imes 10^{-4} $
$ t = \frac{2.8 	imes 10^{-4}}{5.6 	imes 10^{-4}} $
$ t = \frac{2.8}{5.6} $
$ t = 0.5~	ext{s} $
Answer:
Option A: $0.5~	ext{s}$

Answer

0.5 s

Answer

$\quad 0.4 \mathrm{~s}$

Answer

0.8 s

Answer

0.7 s

Electromagnetic Induction

The magnetic flux through a coil is 4 \times 10^{-4} \mathrm{~Wb} at time t=0. It reduces to 30 \% of its original value in time t second. If e.m.f. induced in the coil is 0.56 mV then the value of t is

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