Two coils are wound on the same iron rod so that the flux...

Two coils are wound on the same iron rod so that the flux generated by one passes through the other also. The primary coil has $N_p$ loops and, when a current of 2.0 A flows through it, the flux in it is $2.5 \times 10^{-4} \mathrm{~Wb}$. Determine the mutual inductance of the two coils if the secondary coil has $N$, loops. $$ \left|e_x\right|=N_3\left|\frac{\Delta \Phi_{\mu_2}}{\Delta t}\right| \text { and }\left|\psi_x\right|=M\left|\frac{\Delta i_p}{\Delta t}\right| $$ give $$ M=N_r\left|\frac{\Delta \Phi_{\mathrm{Mb}}}{\Delta t_p}\right|=N, \frac{\left(2.5 \times 10^{-4}-0\right) \mathrm{Wb}}{(2.0-0) \mathrm{A}}=\left(1.3 \times 10^{-4} N_s\right) \mathrm{H} $$

Two coils are wound on the same iron rod so that the flux generated by one passes through the other also. The primary coil has $N_p$ loops and, when a current of 2.0 A flows through it, the flux in it is $2.5 \times 10^{-4} \mathrm{~Wb}$. Determine the mutual inductance of the two coils if the secondary coil has $N$, loops.

$$
\left|e_x\right|=N_3\left|\frac{\Delta \Phi_{\mu_2}}{\Delta t}\right| \text { and }\left|\psi_x\right|=M\left|\frac{\Delta i_p}{\Delta t}\right|
$$

give

$$
M=N_r\left|\frac{\Delta \Phi_{\mathrm{Mb}}}{\Delta t_p}\right|=N, \frac{\left(2.5 \times 10^{-4}-0\right) \mathrm{Wb}}{(2.0-0) \mathrm{A}}=\left(1.3 \times 10^{-4} N_s\right) \mathrm{H}
$$

Key Concepts

Mutual Inductance

Mutual inductance is a measure of the ability of one coil to induce an electromotive force (EMF) in another coil via a shared magnetic flux. It quantifies the coupling between the coils and depends on factors such as the number of turns in each coil, the core material, and the geometry of the magnetic circuit. This concept is fundamental in transformer design and in understanding how energy can be efficiently transferred between circuits.

Magnetic Flux

Magnetic flux represents the total magnetic field passing through a given area, such as a coil's loop, and is measured in webers (Wb). It is a key concept in electromagnetism that determines the amount of magnetic field interacting with the coil, which in turn affects the induced EMF when the magnetic environment changes with time, according to Faraday's law.

Coil Turns (Winding Number)

The number of turns or loops in a coil plays a crucial role in determining the strength of the magnetic effects in electromagnetism. In both self-inductance and mutual inductance, the induced EMF is proportional to the number of turns, making it a critical parameter in designing devices like transformers and inductors where efficient magnetic coupling is required.

Faraday's Law of Electromagnetic Induction

Faraday's law states that a change in magnetic flux through a circuit induces an electromotive force (EMF) in that circuit. This principle underlies the operation of many electrical devices and explains how varying currents in a primary coil can generate an induced voltage in a secondary coil, forming the basis for technologies such as transformers and inductors.

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