Induced Currents

Have you ever wondered how wireless chargers work; how can something transport electrical energy into your phone when it's not even directly plugged in? Or on the other hand, how do induction hobs work when you cook; if there is no fire, how is the hob heating up and cooking your food? Both of these seemingly magical phenomena can be explained by induced forces, whereby an external magnetic field that is changing in strength over time, induces a current into a conducting material. In the case of a wireless charger, the charger generates a changing magnetic field that interacts with a component inside your phone, allowing a current to flow inside it and charge your phone up to full battery! To learn more about induced forces and how to calculate them, keep reading!

Fig. 1 - A wireless charger uses induced forces to charge electrical devices without directly connecting to them

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Induced Current Meaning

Before we get into the meaning of an induced current, we must understand the process of electromagnetic induction and how it occurs. When we have a magnetic field, one of the properties of the magnetic field is its flux. This is defined as the following.

Due to the movement of the magnet or a reduction in the strength of the magnetic field, the magnetic flux of a magnet can change over time. This change in magnetic flux causes the phenomenon of electromagnetic induction.

Furthermore, we can also define the electromotive force in relation to potential difference as the following.

This electromotive force present in the conductive material then causes current to flow, thus resulting in an induced current.

Induced Current Formula

Firstly, let's consider the formula for the magnetic flux of a field. This is given by

\[ \Phi_{\text{B}} = \int \vec{B} \cdot \mathrm{d} \vec{A} ,\]

where \( \Phi_{\text{B}} \) is the magnetic flux of a magnetic field measured in weber (\(\mathrm{Wb}\)), \(\vec{B}\) is the magnetic field vector measured in units of teslas (\(\mathrm{T}\)), and \(\mathrm{d} \vec{A}\) is the infinitesimal area vector measured in \(\mathrm{m^2}\). From the equation, the dot product highlights that we are only considering the component of the magnetic field perpendicular to the area.

Now that we have defined the magnetic flux, we can define the equation for electromagnetic induction as the following,

\[ \varepsilon = - \frac{\mathrm{d} \Phi_{\text{B}}}{\mathrm{d} t}, \]

where \(\varepsilon\) is the induced electromotive force measured in volts \(\mathrm{V}\), \(\Phi_{\text{B}}\) is the magnetic flux measured in webers \(\mathrm{Wb}\), and \(t\) is time measured in seconds \(\mathrm{s}\). This law is governed by two laws: Faraday's law and Lenz's law. The former determines the magnitude of the induced electromotive force, whilst the latter determines the direction of the induced current.

Let's consider an example where we use our electromagnetic induction formula.

Direction of Induced Current

As we mentioned briefly earlier, the direction of the induced electromotive force in electromagnetic induction is determined using Lenz's law.

Fig. 3 - When the magnet enters the tube, it experiences an upward force due to Lenz's law.

Referring to the figure above, let's consider a magnet being dropped through a tube made of conducting material. As the magnet falls, there is an induced current in the aluminum material. As current runs through it, the tube itself generates its own magnetic field. However, this time, the direction of the magnetic field is opposite in direction to that of the magnet falling through the tube. To determine whether the current flowing in the tube is clockwise or anticlockwise, we can use the right-hand rule.

To use this method, curl the fingers on your right hand as if you are enclosing a tube. The direction of your fingers should follow the direction of the induced current. Then extend out your thumb; the direction your thumb is pointing indicates the north pole of the conductor, as the current has essentially turned the conductor into a magnet. Since we know that the conductor must repel the falling magnet, this means that the north pole of the conductor must be pointing upwards to repel the falling magnet with a like pole. Pointing our thumb upwards, we find that the resultant curl of our fingers is in the counter-clockwise direction, which is the direction of the induced current in the tube. This repels the north pole of the magnet from being dropped into the tube, thus creating an opposing force that reduces the acceleration.

The right-hand grip rule can also be used to determine the direction of the magnetic field generated by a current running through a wire. In this case, the thumb points in the direction of the current, whilst the direction of your fingers indicate the curvature of the generated magnetic field.

Difference between Current and Induced Current

Normal current occurs when we have a typical circuit set-up with a power source connected to a resistor. Referring to the figure below, we have a connected circuit with conventional current \(I\) flowing through the resistors due to the power source.

Fig. 5 - A standard circuit set-up with conventional current flowing through the components and the wires.

On the other hand, an induced current is generated from an external changing magnetic flux. As we saw earlier, examples of induced current can occur when a magnet falls through a conductive tube or a magnet moves next to a conductive material. Examples of the applications of inductive current are seen in wireless chargers and induction stoves.

Geomagnetically Induced Currents

A large-scale example of induced forces is geomagnetically induced currents, also referred to as GICs. Just like how magnets have their own surrounding magnetic fields, our Earth also has an enormous magnetic field surrounding the globe. This field is generated by the convection of radioactive heating at our Earth's core. Thus, our North pole and South pole behave exactly like the north and south poles of a magnet.

Changes in the Earth's surrounding magnetic field are caused by space weather events such as solar wind. Fluctuations in the field behave like a moving magnet, changing the flux of the magnetic field over time. Thus any conductive material on the surface of the Earth, such as gridlines or pipelines, will have a current induced in them as a result of the changing field. This can negatively affect the machinery and cause damage to electrical transmissions.