UY1: Mutual Inductance

Consider two neighboring coils of wire. A current $i_{1}$ flowing in coil 1 produces a magnetic field $\vec{B}$ and hence a magnetic flux $\Phi_{B2}$ is produced through each turn of coil 2. From Faraday’s Law, $$\epsilon_{2} =-N_{2} \frac{d \Phi_{B2}}{dt}$$ Now, we shall introduce a quantity, mutual inductance to relate the magnetic flux through coil 2 with the current in coil …

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UY1: Displacement Current

Consider the process of charging a parallel-plate capacitor. Conducting wires lead (conduction) current $i_{C}$ into one plate and out of the other. The charge q increases, and the electric field between the plates increases. Recall that: (for a parallel-plate capacitor) $$\begin{aligned} q &= Cv \\ C &= \epsilon \frac{A}{d} \\ E &= \frac{v}{d} \end{aligned}$$ Let’s compute $i_{C}$, $$\begin{aligned} i_{c} &= …

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UY1: Motional Electromotive Force

Consider a rod of length L moving through a magnetic field as shown below: A positively charged particle q in the rod experiences a magnetic force: $$\vec{F} = q \vec{v} \times \vec{B}$$ Charge will continue to accumulate at the ends of the rod until the electric field $\vec{E}$ within the rod satifies: $$qE = qvB$$ Hence, the voltage difference of …

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UY1: Examples Involving Faraday’s Law

Example: A Simple Alternator A rectangular loop is made to rotate with constant angular speed $\omega$ about the axis shown. The magnetic field $\vec{B}$ is uniform and constant. Find the induced e.m.f. The induced e.m.f. is given by: $$\begin{aligned} \epsilon &=-\frac{d \Phi_{B}}{dt} \\ &=-\frac{d}{dt} \left( BA \cos{\omega t} \right) \\ &= \omega BA \sin{\omega t} \end{aligned}$$ Example: Slidewire Generator Consider …

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UY1: Faraday’s Law Of Induction & Lenz’s Law

Faraday’s Law of Induction Faraday’s law of induction states that the induced e.m.f. in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. $$\epsilon =- \frac{d\Phi_{B}}{dt}$$ Example: E.M.F. and current induced in a loop The magnetic field between the poles of the electromagnet is uniform at any time, but its magnitude …

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UY1: Electromagnetic Induction Experiments

Basics of Electromagnetic Induction Consider a coil of wire connected to a galvanometer. When the nearby magnet is stationary, the meter shows no current. When we move the magnet either towards or away from the coil, the meter shows current in the circuit, while the magnet is moving. Now, we replace the magnet with a solenoid that is connected to …

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