Electromagnetic Induction

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The magnitude of the induced emf in a coil is equal to the rate of change of magnetic flux linked with the coil. Mathematically: $$ |\varepsilon| = \frac{d\phi_B}{dt} $$ For a coil of N turns: $$…

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Step 1: Area of coil = $\pi r^2 = \pi (0.1)^2 = 0.0314\,\mathrm{m^2}$ Step 2: Change in magnetic field = $\Delta B = 0.6 - 0.2 = 0.4\,\mathrm{T}$ Step 3: Rate of change of flux per turn = $\frac{d\p…

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Lenz's Law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. This ensures conservation of energy. Example: When a north pole of a …

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As the north pole approaches the coil, the magnetic flux through the coil increases in the direction of the magnet's field. By Lenz's Law, the induced current will oppose this increase. So, the side …

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Magnetic flux ($\phi_B$) is the total number of magnetic field lines passing normally through a given surface area. Mathematically: $$ \phi_B = \vec{B} \cdot \vec{A} = B A \cos\theta $$ Where: - $…

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Given: - $B = 0.5\,\mathrm{T}$ - $A = 0.2\,\mathrm{m^2}$ - $\theta = 60^\circ$ Formula: $\phi_B = B A \cos\theta$ Step 1: $\cos 60^\circ = 0.5$ Step 2: $\phi_B = 0.5 \times 0.2 \times 0.5 = 0.05\,\…

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The combined form includes the negative sign to indicate opposition to change: $$ \varepsilon = -\frac{d\phi_B}{dt} $$ For a coil of N turns: $$ \varepsilon = -N \frac{d\phi_B}{dt} $$ The negative…

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Step 1: Change in flux per turn = $\Delta\phi = 0.08 - 0.02 = 0.06\,\mathrm{Wb}$ Step 2: Rate of change = $\frac{d\phi}{dt} = \frac{0.06}{0.2} = 0.3\,\mathrm{Wb/s}$ Step 3: Induced emf = $N \cdot \f…