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Physics Chapter 12 : Topic 15
Electromagnetic Induction Problems
1 / 30
Faraday’s law of electromagnetic induction is mathematically expressed as:
Reasoning: Faraday’s law states that induced $\mathbf{e.m.f.}$ is equal to the rate of change of magnetic flux linkage. The negative sign represents Lenz’s law.
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A coil has $\mathbf{200}$ turns. The magnetic flux through each turn changes from $\mathbf{0.5\ Wb}$ to $\mathbf{0.1\ Wb}$ in $\mathbf{2}$ seconds. The magnitude of induced $\mathbf{e.m.f}$ is:
Reasoning: $\mathbf{E =}$ $\frac{\mathbf{N\Delta\Phi}}{\mathbf{\Delta t}}$ $\Longrightarrow$ $\mathbf{E =}$ $\frac{\mathbf{200\ (0.5\ - \ 0.1)}}{\mathbf{2}}\mathbf{= 40\ V}$
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The negative sign in Faraday’s law indicates that:
Reasoning: The negative sign represents Lenz’s law, which determines the direction of induced current.
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A coil of $\mathbf{100}$ turns experiences a change in magnetic flux of $\mathbf{0.02\ Wb}$ in $\mathbf{0.5}$ seconds. The induced $\mathbf{e.m.f.}$ is:
Reasoning: $\mathbf{E =}$ $\frac{\mathbf{N\Delta\Phi}}{\mathbf{\Delta t}}$ $\Longrightarrow$ $\mathbf{E =}$ $\frac{\mathbf{100\ (0.02)}}{\mathbf{0.5}}\mathbf{= 4\ V}$
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If the time taken for a given change in magnetic flux is reduced, the induced $\mathbf{e.m.f}$:
Reasoning: Induced $\mathbf{e.m.f.}$ depends on the rate of change of flux: $\mathbf{E \propto}$ $\frac{\mathbf{\Delta\Phi}}{\mathbf{\Delta t}}$
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A magnet is moved toward a coil. According to Lenz’s law, the coil:
Reasoning: The induced magnetic field opposes the change in magnetic flux, causing repulsion.
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A coil has $\mathbf{500}$ turns. If the flux linkage changes by $\mathbf{100\ Wb\ }$in $\mathbf{5}$ seconds, the induced $\mathbf{e.m.f.}$ is:
Reasoning: Flux linkage change: $\mathbf{\Delta}\left( \mathbf{N\Phi} \right)\mathbf{= 100\ Wb}$ $\Longrightarrow$ $\mathbf{E =}$ $\frac{\mathbf{100}}{\mathbf{5}}\mathbf{= 20\ V}$
8 / 30
A generator produces electricity because:
Reasoning: A generator works on electromagnetic induction, where changing flux linkage produces $\mathbf{e.m.f}$.
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A coil is rotated in a magnetic field. The induced $\mathbf{e.m.f}$ is maximum when:
Reasoning: According to Faraday’s law, maximum $\mathbf{e.m.f.}$ occurs when the rate of change of flux is maximum.
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A coil of $\mathbf{50}$ turns has flux changing from $\mathbf{(4\ Wb)}$ to $\mathbf{(1\ Wb)}$ in $\mathbf{3}$ seconds. The induced $\mathbf{e.m.f.}$ is:
Reasoning: $\mathbf{E =}$ $\frac{\mathbf{N\Delta\Phi}}{\mathbf{t}}$ $\Longrightarrow$ $\mathbf{E =}$ $\frac{\mathbf{50(4\ - \ 1)}}{\mathbf{3}}\mathbf{= 50\ V}$
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If the number of turns in an induction coil is doubled, induced $\mathbf{e.m.f}$:
Reasoning: $\mathbf{E \propto N}$ $\Longrightarrow$ More turns produce greater flux linkage change.
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A coil is connected to a galvanometer. The galvanometer deflects because:
Reasoning: Changing magnetic flux induces an $\mathbf{e.m.f}$, which produces current in the circuit.
13 / 30
A magnetic flux through a coil changes from $\mathbf{2\ Wb}$ to $\mathbf{8\ Wb}$ in $\mathbf{2}$ seconds. For a single turn coil, induced $\mathbf{e.m.f}$ is:
Reasoning: $\mathbf{E =}$ $\frac{\mathbf{\Delta\Phi}}{\mathbf{t}}$ $\Longrightarrow$ $\mathbf{E =}$ $\frac{\mathbf{8\ - \ 2}}{\mathbf{2}}\mathbf{= 3\ V}$
14 / 30
If there is no change in magnetic flux through a coil, induced $\mathbf{e.m.f.}$ is:
Reasoning: Faraday’s law requires a change in magnetic flux for induction.
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According to Lenz’s law, when magnetic flux through a coil increases, induced current produces a magnetic field that:
Reasoning: The induced field always opposes the change in flux.
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A coil has $\mathbf{300}$ turns and an induced $\mathbf{e.m.f.}$ of $\mathbf{60\ V}$. If flux changes uniformly in $\mathbf{2}$ seconds, the change in flux is:
Reasoning: $\mathbf{E =}$ $\frac{\mathbf{N\Delta\Phi}}{\mathbf{t}}$ $\Longrightarrow$ $\mathbf{60 =}$ $\frac{\mathbf{300\ \Delta\Phi}}{\mathbf{2}}$ $\Longrightarrow$ $\mathbf{\Delta\Phi = 0.4\ Wb}$
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The induced current in a coil depends on:
Reasoning: $\mathbf{I =}$ $\frac{\mathbf{E}}{\mathbf{R}}$ $\Longrightarrow$ The current depends on induced voltage and resistance.
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A stronger magnet moving at the same speed through a coil produces:
Reasoning: A stronger magnet causes a larger change in magnetic flux.
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A coil has $\mathbf{1000}$ turns. The magnetic flux changes by $\mathbf{5 \times}\mathbf{10}^{\mathbf{- 3}}\mathbf{\ Wb}$ in $\mathbf{0.1\ s}$. The induced $\mathbf{e.m.f.}$ is:
Reasoning: $\mathbf{E =}$ $\frac{\mathbf{N\Delta\Phi}}{\mathbf{t}}\mathbf{=}\frac{\mathbf{1000\ \times \ (5\ \times \ }\mathbf{10}^{\mathbf{- 3}}\mathbf{)}}{\mathbf{0.1}}$ $\Longrightarrow$ $\mathbf{E = 50\ V}$
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A magnet is pulled away from a coil. The coil’s near face becomes:
Reasoning: The coil opposes the decrease in flux by attracting the departing magnet.
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Which change will increase induced $\mathbf{e.m.f}$?
Reasoning: Faster flux change produces greater induced $\mathbf{e.m.f}$.
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The induced $\mathbf{e.m.f}$ in a rotating coil changes continuously because:
Reasoning: Rotation changes the angle between coil and magnetic field, changing flux linkage.
23 / 30
A coil experiences a flux change of $\mathbf{0.1\ Wb}$ in $\mathbf{0.01\ }\mathbf{s}$. The induced $\mathbf{e.m.f.}$ in one turn is:
Reasoning: $\mathbf{E =}$ $\frac{\mathbf{\Delta\Phi}}{\mathbf{\Delta t}}$ $\mathbf{\Longrightarrow}$ $\mathbf{E =}$ $\frac{\mathbf{0.1}}{\mathbf{0.01}}\mathbf{= 10\ V}$
24 / 30
A coil with $\mathbf{200}$ turns has induced $\mathbf{e.m.f}\mathbf{.}$ $\mathbf{40\ V}$. If the rate of change of flux is constant, a coil with $\mathbf{4}\mathbf{00}$ turns will produce:
Reasoning: Doubling turns doubles induced $\mathbf{e.m.f}$.
25 / 30
Eddy currents are produced because of:
Reasoning: Changing magnetic flux induces circulating currents in conductors.
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The direction of induced current is determined by:
Reasoning: Lenz’s law gives the direction of induced current.
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A coil is moved faster through a magnetic field. The induced $\mathbf{e.m.f.}$ increases because:
Reasoning: Faster movement increases rate of change of magnetic flux.
28 / 30
A transformer works on the principle of:
Reasoning: Transformers use changing magnetic flux to induce $\mathbf{e.m.f}$.
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If the induced current supports the change causing it, it would violate:
Reasoning: Supporting the change would create energy without input, violating energy conservation.
30 / 30
The magnitude of induced $\mathbf{e.m.f.}$ increases with:
Reasoning: Faraday’s law shows $\mathbf{e.m.f.}$ depends on the rate of change of flux linkage.
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