Question

A coil of circular cross-section having 1000 turns and 4 cm2 face area is placed with its axis parallel to a magnetic field which decreases by 10-2 Wb m-2 in 0.01 s. The e.m.f. induced in the coil is :

Answer 1

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Answer 2

Answer:

0.4 Volts.

Explanation:

Given:

• Number of turns of the coil, N = 1000 turns.
• Cross-sectional area of the coil, A = $\rm 4\ cm^2 = 4\times 10^{-4}\ m^2.$
• Change in magnetic field, dB = $\rm -10^{-2}\ Wb\ m^{-2}.$
• Time period in which the magnetic field changes, dt = 0.01 s.

Here, dB is taken to be negative because the magnetic field is decreased.

The magnetic flux linked with the coil is given by

$\phi = N\vec B \cdot \vec A=\rm NBA\cos\theta.$

where $\vec A$ is the area vector of the coil, directed along the axis of the coil and $\theta$ is the angle between magnetic field and the area vector of the coil.

Since the coil is placed with its axis parallel to a magnetic field, therefore, $\theta=0^\circ.$

$\rm \phi = NBA\cos0^\circ=NBA.$

According to the Faraday's law of electromagnetic induction, the emf induced in the coil is given by

$\rm e = -\dfrac{d\phi }{dt}\\=-\dfrac{d(NBA)}{dt}\\=-NA\dfrac{dB}{dt}\\=-(1000)\times (4\times 10^{-4})\times \dfrac{-10^{-2}}{0.01}\\=0.4\ V.$