Question 56: Electromagnetic Induction

Question

Three identical coils $C_1, C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current $I$ in anti-clockwise direction while $C_3$ carries current $I$ in clockwise direction. An induced current flows through $C_2$ will be in clockwise direction when

Accepted Answer

Looking at the coils along their common axis from the right side looking left).
Coil $\mathrm{C}_1$ carries current in the anti-clockwise ( ACW ) direction. According to the Right-Hand Grip Rule, an ACW current produces a magnetic field $\left(\overrightarrow{\mathrm{B}}_1ight)$ pointing towards the observer.
Let's define this direction towards the observer as positive flux.
Coil $\mathrm{C}_3$ : Carries current in the clockwise (CW) direction. An ACW current produces a magnetic field ( $\overrightarrow{\mathrm{B}}_3$ ) pointing away from the observer.
Let's define this direction pointing away from the observer as negative flux.
Coil $C_2$ is exactly in the middle. Because $C_1$ and $C_3$ are identical and carry the same magnitude of current $I$, the strength of their magnetic fields at the midpoint will be identical.
Since $\vec{B}$ points towards us and $\vec{B}_3$ points away from us with equal magnitudes, they cancel each other out.
Initial Net Magnetic Flux through $\mathrm{C}_2$ is $\Phi_{	ext {initial }}=0$
A clockwise current in $\mathrm{C}_2$ would create its own induced magnetic field $\left(\overrightarrow{\mathrm{B}}_{	ext {induced }}ight)$ pointing away from the observer i.e., negative direction.
Lenz's Law states that an induced current will always flow in a direction that opposes the change in magnetic flux that caused it.
Since the induced field points in the negative direction, it must be resisting a change in the positive direction.
Therefore, the external magnetic flux through $\mathrm{C}_2$ must be increasing in the positive direction (towards the observer).
To get a net increase in positive flux, we have two ways :
Increase the positive flux from $\mathrm{C}_1$ by moving the source of the positive flux $\left(\mathrm{C}_1ight)$ closer to $\mathrm{C}_2$.
Decrease the negative flux from $\mathrm{C}_3$ by moving the source of the negative flux $\left(\mathrm{C}_3ight)$ further away from $\mathrm{C}_2$.
Therefore, $C_1$ moves towards $C_2$ (increases positive flux) and $C_3$ moves away from $C_2$ (decreases negative flux). This results net positive flux change required to induce a clockwise current.
Hence, the correct option is (B).

Answer

$C_1$ and $C_3$ move with equal speeds away from $C_2$

Answer

$C_1$ moves towards $C_2$ and $C_3$ moves away from $C_2$

Answer

$C_1$ and $C_3$ move with equal speeds towards $C_2$

Answer

$C_1$ moves away from $C_2$ and $C_3$ moves towards $C_2$

Electromagnetic Induction

Three identical coils C_1, C_2 and C_3 are closely placed such that they share a common axis. C_2 is exactly midway. C_1 carries current I in anti-clockwise direction while C_3 carries current I in clockwise direction. An induced current flows through C_2 will be in clockwise direction when

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