Induced Current

Induced Current occurs whenever Electromagnetic Induction occurs. More specifically, if the conductor is a circuit (a loop of wire), then a strong current can be generated. Else, if the current has no well-defined path, it forms loops of Eddy Currents on the conducting surface.

From Motional EMF §

The Motional EMF generated from a moving rod can be expanded to generate an induced current.

Let’s look back to our moving rod in a magnetic field

It has a voltage, but no path for the current to flow through. What if we provide a static (non-moving) rectangular conducting rail?

Recall Ohm’s Law and Motional EMF:

So our current is:

$$I=\frac{\mathcal{E}}{R}=\frac{l\vec{v}\times \vec{B}}{R}=\frac{Bvl}{R}(\text{as B⊥v})$$

However, because we now have a current (and not just voltage), we have a new magnetic field being generated:

Since we defined the conducting rail to be static, only the rod can move. What would be the magnetic force on the rod?

Using the Right Hand Rule, we can determine the induced magnetic force, ${F_B}_{induced}$ is opposing the direction of motion. Since $F=ma$, we know that this force will decelerate the rod, eventually causing it to halt. In order to keep it moving, we need an external force, $F_{ext}$, exactly equal in magnitude, to keep the rod moving at the same speed:

$$F_{ext}=-F_B$$

Conservation of Energy in a §

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Power Dissapation §

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