Question 196: Electromagnetic Induction

Question

A coil of effective area $3 \mathrm{~m}^2$ is placed at right angles to a magnetic field of induction $0.05 \mathrm{~Wb} / \mathrm{m}^2$ If the field is decreased to $20 \%$ of its original value in 10 second, the e.m.f. induced in the coil will be

Accepted Answer

Identify the given values:
Effective Area (A) = $3 \mathrm{~m}^2$
Initial Magnetic Field Induction ($B_1$) = $0.05 \mathrm{~Wb} / \mathrm{m}^2$
Final Magnetic Field Induction ($B_2$) = $20\%$ of $B_1 = 0.20 	imes 0.05 \mathrm{~Wb} / \mathrm{m}^2 = 0.01 \mathrm{~Wb} / \mathrm{m}^2$
Time taken for the change ($\Delta t$) = $10 \mathrm{~s}$
The coil is placed at right angles to the magnetic field, meaning the angle between the normal to the coil's area and the magnetic field is $0^\circ$. So, $\cos	heta = \cos 0^\circ = 1$.
Calculate the initial magnetic flux ($\Phi_1$):
Magnetic flux ($\Phi$) = $B 	imes A 	imes \cos	heta$
$\Phi_1 = B_1 	imes A 	imes 1$
$\Phi_1 = 0.05 \mathrm{~Wb} / \mathrm{m}^2 	imes 3 \mathrm{~m}^2$
$\Phi_1 = 0.15 \mathrm{~Wb}$
Calculate the final magnetic flux ($\Phi_2$):
$\Phi_2 = B_2 	imes A 	imes 1$
$\Phi_2 = 0.01 \mathrm{~Wb} / \mathrm{m}^2 	imes 3 \mathrm{~m}^2$
$\Phi_2 = 0.03 \mathrm{~Wb}$
Calculate the change in magnetic flux ($\Delta\Phi$):
$\Delta\Phi = \Phi_2 - \Phi_1$
$\Delta\Phi = 0.03 \mathrm{~Wb} - 0.15 \mathrm{~Wb}$
$\Delta\Phi = -0.12 \mathrm{~Wb}$
Apply Faraday's Law of Electromagnetic Induction:
The induced e.m.f. ($\varepsilon$) is given by:
$\varepsilon = -N \frac{\Delta\Phi}{\Delta t}$
Assuming $N=1$ (single turn coil, as not specified otherwise):
$\varepsilon = - \frac{\Delta\Phi}{\Delta t}$
$\varepsilon = - \frac{-0.12 \mathrm{~Wb}}{10 \mathrm{~s}}$
$\varepsilon = \frac{0.12}{10} \mathrm{~V}$
$\varepsilon = 0.012 \mathrm{~V}$
Convert the e.m.f. to millivolts (mV):
$1 \mathrm{~V} = 1000 \mathrm{~mV}$
$\varepsilon = 0.012 \mathrm{~V} 	imes 1000 \mathrm{~mV/V}$
$\varepsilon = 12 \mathrm{~mV}$
The induced e.m.f. in the coil will be $12 \mathrm{~mV}$.
The final answer is $\boxed{	ext{12 mV}}$.

Answer

10 mV

Answer

12 mV

Answer

15 mV

Answer

20 mV

Electromagnetic Induction

A coil of effective area 3 \mathrm{~m}^2 is placed at right angles to a magnetic field of induction 0.05 \mathrm{~Wb} / \mathrm{m}^2 If the field is decreased to 20 \% of its original value in 10 second, the e.m.f. induced in the coil will be

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