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An Electric Field from a Changing Magnetic Field
It is sometimes difficult to define what a field is in physics, but typically we define electric fields as follows:
An electric field is a field of space in which an object can experience an electric force.
Electric fields can be created by changing magnetic fields. In other words, if the amplitude of the magnetic field is changing over time, then an electric field will be induced. This is explored further in the example below.
The magnitude of the magnetic field, \(B\), is increasing over time. The arrows on our ring show that we have a current, \(I\), moving in a counterclockwise direction, and the crosses on the diagram show the magnetic field is directed out of the screen.
Wire conductor in an increasing magnetic field,StudySmarter Originals.
When we have a wire loop inside of a changing magnetic field we observe a current in the loop. This means the charges are experiencing an electric force. From this, we can conclude that the changing magnetic field has created an induced electric field which has caused current to flow.
But what is the shape of that field? The fact that there is a current moving in the circular wire gives us a hint that it can be a circular electric field. We also know that the electric field lines must be closed loops. Thus the image below shows what our induced electric field looks like
Multiple conducting wires in an external changing magnetic field, StudySmarter Originals.
The process occurs by first introducing a changing magnetic flux in a wire. This in turn will induce an electric field, which induces voltage in the wire. Finally, the voltage induces current in the wire.
The electric field will be induced even if there is no loop wire.
However, in this case, there is no induced current.
The varying magnetic field will create an electric field even if there is no wire or conductor. However, if there is no wire then there are no charges to apply electric force on. Thus, neither voltage nor current will be induced.
A Changing Electric Field produces a Magnetic Field
The above example works in the opposite direction as well. If we induce a current in our ring using a power source, we will observe a magnetic field around our ring.
Current Induced by a Changing Magnetic Field
As discussed earlier, a changing magnetic field would always induce an electric field.
However only when there is a conductor in a changing magnetic field:
Then, an electric field will be induced.
Causing an induced voltage on the conductor.
As a result, a current will flow in the conductor.
The induced voltage cannot occur if there is no conductor in the region of the changing magnetic field.
Here are some interesting queries we can make about a magnetic field:
How would heating a bar magnet would change its magnetic field?
- When the atoms in the magnet are heated: They gain kinetic energy and travel faster.
- Because the atoms are moving so quickly: They clash with other atoms, causing domain atoms to become misaligned.
- The magnetic field would be reduced as a result.
How often does earth's magnetic field change direction?
- The Earth's magnetic field has experienced countless polarity reversals over geological time.
- There have been 4 or 5 reversals every million years on average in the previous 10 million years.
How does the magnetic field change with distance?
- Magnetic dipoles, which use either permanent magnets or current-carrying wire loops, are commonly used to generate magnetic fields. Every magnet is surrounded by a magnetic field.
- When an item enters the magnetic field, it is drawn in by the magnet. As the distance between them decreases, the attraction rises. As a result, the magnetic force is stronger when the distance is smaller.
The Rate of Change of a Magnetic Field
The induced voltage in a circuit is proportional to the rate of change of the magnetic flux over time:
First, note that the magnetic flux is defined as the number of field lines passing through a given area and is a way of looking at the total magnetic field in that area. Then we can say the induced voltage in a circuit is propotional to the rate of change of the magnetic flux over time,
\[V\propto\Delta \Phi\]
In other words, the higher the voltage in the circuit, the faster the magnetic field changes. Here, The direction of the current is determined by the direction of the magnetic field change.
If we wish to increase this voltage, we can add more loops to the circuit. The induced voltage in a coil with two loops will be double that of a coil with one loop, and it will be tripled in a coil with three loops. This is why motors and generators have a lot of coils in them.
A Wave of Changing Electric and Magnetic Fields:
As discussed earlier, a changing magnetic field would induce an electric field. This means that a magnetic field will create an electric field if it oscillates as a function of time. Similarly, an electric field will also produce a magnetic field if it changes as a function of time. In an electromagnetic wave, both the electric and magnetic fields will fluctuate over time, with one influencing the other to shift.
The changing electric and magnetic fields can be illustrated in the figure below:
Illustration of an electromagnetic wave,Wikimedia Commons, CC BY-SA 4.0
As you can see in the figure above, the electric and magnetic fields in an electromagnetic wave are changing. However, the electric and magnetic waves will always be perpendicular to each other and to the direction of propagation of motion.
Changing Magnetic Fields - Key takeaways
If the amplitude of the magnetic field is changing with time, then an electric field will be induced.
The induced electric field will induce a voltage on the conducting wire, thus a current will pass in the wire.
The electric field will be induced even if there is no loop wire. However, in this case there is no induced current.
The induced voltage in a circuit is proportional to the rate of change of the magnetic flux over time.
In other words, the higher the voltage in the circuit, the faster the magnetic field changes.
The direction of the current is determined by the direction of the magnetic field change.
By adding more loops to the circuit, we may raise the voltage.
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Frequently Asked Questions about Changing Magnetic Field
What does a changing magnetic field induce?
A changing magnetic field induces a current in a wire.
How often does earths magnetic field change direction?
Earths magnetic field changes direction over a period of about 300,000 years.
How do you change a magnetic field?
You can change a magnetic field by increasing or decreasing the size of the loop of wire being used to induce the magnetic field.
How would heating a bar magnet change its magnetic field?
Heating a bar magnet would reduce the magnetic field strength it produces.
How does a magnetic field change with distance?
A magnetic field gets weaker the farther it travels.
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