In this explainer, we will learn how to describe the magnetic field that is produced by a wire carrying an electric current.
If there is a net flow of charge along a wire, there is a current in the wire. The diagram below shows a long, straight wire carrying a current.
The current creates a magnetic field around itself. The field lines, shown below, form circles around the wire.
The magnetic field formed by the current exists everywhere around the wire. Circular field lines form around it, extending to any distance out from the wire.
If we change our perspective to look along the wire from one end, the current could point directly toward us as shown below. Viewed this way, we say the current points “out of the screen” or “out of the screen.”
This figure shows the symbol for current pointing out of the screen: a circle with a dot in the center. It also shows that magnetic field lines at different distances from the wire form concentric circles.
As distance from the wire increases, the circles are spaced farther apart. This indicates a decreasing magnetic field strength.
Instead of viewing a current pointing out of the screen toward us, it is possible to view it pointing the opposite way: “into the screen.” A current in this direction is symbolized by a circle around an X, as shown below.
Notice that the magnetic field in this figure points clockwise around the wire, while the field in the figure with a current pointing out of the screen points counterclockwise.
To determine the direction of the magnetic field around a current-carrying wire, we use what is called the “right-hand rule.” This rule states that if we point the thumb of our right hand in the direction of the current in a straight wire, the direction our fingers curl (say to grip something) is the direction of the magnetic field around that wire.
This method applies for wires carrying current into and out of the screen, as shown below.
In both cases, when we point our right thumb in the direction of the current in the wire, our fingers curl in the direction of the magnetic field created by the current.
Example 1: Understanding the Magnetic Field Created by a Current-Carrying Wire
Which of the four diagrams correctly shows the field lines of the magnetic field created around a current-carrying wire?
To answer this question, we will use what is called the “right-hand grip rule.” This rule states that the direction of the magnetic field formed by an electrical current is given by the direction our fingers curl when the thumb of our right hand points in the same direction as the current.
We can apply this rule to the four cases (A), (B), (C), and (D), in order.
For scenario (A), we point our right thumb into the screen since the current points in that direction. Curling our fingers, we find they move in a clockwise arc. This goes against the indicated counterclockwise magnetic field direction. Therefore, diagram (A) does not correctly show magnetic field lines around the current-carrying wire.
In scenario (B), the current points out of the screen. When the thumb of our right hand points that way, our fingers curl in a counterclockwise direction. This goes against the indicated clockwise magnetic field direction in the diagram. Diagram (B) also does not correctly show the magnetic field created around the current-carrying wire.
Scenario (C) has current pointing into the screen and clockwise magnetic field direction. Testing this with our right-hand grip rule, we find that indeed our fingers do curl clockwise when our right thumb points into the screen. Diagram (C) is correct!
Considering scenario (D), we see that part of the magnetic field points counterclockwise and part clockwise. This is not physically possible, so we know diagram (D) is not a correct depiction of the magnetic field around a current-carrying wire.
Our final option is diagram (C).
We have noted that the strength of the magnetic field created by a current-carrying wire gets weaker as distance from the wire increases.
Another factor affecting the strength of the field is the magnitude of the current creating it. The stronger the current (the larger its magnitude), the stronger the magnetic field.
Example 2: Understanding Magnetic Fields Produced by Electric Currents
For the magnetic field created around a current-carrying wire, the the current, the the magnetic field.
- larger, weaker
- smaller, stronger
- larger, stronger
There is a direct relationship between the magnitude of the electric current creating a magnetic field and the magnitude of the field itself.
We can say therefore that the larger the current, the stronger the field, and the smaller the current, the weaker the field.
Both of these descriptions correctly fill in the blanks of the sentence, but only one of them is offered as an option. Option (C), “larger, stronger,” would result in a sentence that reads “For the magnetic field created around a current-carrying wire, the larger the current, the stronger the magnetic field.” This correctly completes the sentence, so our final option is option (C).
A wire carrying current can be straight, as we have considered so far, but it can also be arranged in a coil, as shown in the following figure.
A coil of wire like this is known as a solenoid. Like any other shape of wire, when a solenoid carries a current, it produces a magnetic field around itself.
Interestingly, the magnetic field of a solenoid looks very much like the magnetic field created by a bar magnet.
When a solenoid carries a current, the magnetic field inside its coils is quite strong, while the field outside is relatively weak.
It is possible to strengthen the magnetic field inside the solenoid by putting a material that can be magnetized into the solenoid’s core.
A magnetizable material is one that, when placed in a magnetic field, becomes a magnet itself and creates its own magnetic field.
An example of such a material is iron. If a cylinder of iron is placed within the solenoid, as shown below, the field due to the solenoid magnetizes the iron, which then develops its own magnetic field, which in turn enhances the field of the solenoid.
Example 3: Identifying a Solenoid
Each of the following diagrams shows an object made of copper. Which object is a solenoid?
A solenoid is made of wire that can carry current. Importantly, the wire in a solenoid is continuous, meaning charge can flow from one end of the solenoid to the other.
The wire in a solenoid is also coiled to create many turns that are parallel to one another.
Options (A) and (B) show disconnected loops of wire. Since they are not continuous, neither of these options shows a solenoid.
Option (C) shows wire loops linked together. The loops are not arranged parallel to one another, so we will not choose option (C) either.
Option (E) depicts a hollow cylinder. Since this is not constructed from a single segment of wire, it is not a solenoid.
Knowing that a solenoid is made of a continuous length of wire arranged in parallel loops eliminates all options except option (D).
Example 4: Knowing Key Terms Related to Electromagnetism
Which of the following is the correct description of a solenoid?
- A solenoid is a single straight piece of wire. Passing an electric current along it creates a magnetic field around it.
- A solenoid is a single loop of insulated wire. Passing an electric current through it creates a magnetic field similar to that of a bar magnet.
- A solenoid is a long coil of insulated wire. Passing an electric current through it creates a magnetic field similar to that of a bar magnet.
Considering these three candidate descriptions, we see they differ primarily over the shape of the wire that makes a solenoid.
A solenoid is not a straight piece of wire; consists of a series of loops called a coil. The more loops in the coil, the stronger the magnetic field it creates.
When electric charge flows through a solenoid, it creates a field very similar to the magnetic field due to a bar magnet.
This description corresponds to option (C).
Example 5: Understanding Solenoids
Which two of the following are ways to increase the strength of the magnetic field created by a solenoid?
- Increasing the width of the solenoid
- Decreasing the length of the solenoid
- Increasing the current through the solenoid
- Decreasing the number of turns in the solenoid
- Adding an iron core to the solenoid
We recall that a solenoid is a coil of wire with many turns.
The magnetic field created by the solenoid is effectively the sum of the magnetic fields created by each single loop. The more loops there are, the greater this sum will be and the stronger the overall field.
Therefore, option (D), “Decreasing the number of turns in the solenoid,” cannot be correct. Decreasing the number of solenoid turns will actually weaken the total magnetic field.
Likewise, option (B), “Decreasing the length of the solenoid,” does not describe a way to strengthen the solenoid’s magnetic field. Decreasing a solenoid’s length will effectively remove turns from the coil, again weakening the overall field.
Option (A) claims that increasing a solenoid’s width will increase its magnetic field strength. However, it is the number of loops, and not their diameter, that affects the magnetic field strength in a solenoid.
Regarding ways to increase a solenoid’s field strength, one approach that works for current-carrying wires of any shape is to increase the current in the wire. This corresponds to option (C).
Finally, inserting a magnetic material such as iron into a solenoid’s core will add to the field in the core, increasing its magnitude.
Options (C) and (E) are two ways of increasing a solenoid’s magnetic field strength.
- A current-carrying wire creates a magnetic field.
- In such a field, the magnetic field lines form circles centered on the wire.
- The direction of the magnetic field generated by a current is determined by the “right-hand rule.”
- A solenoid is a coil of wire.
- When carrying current, a solenoid produces a magnetic field similar to the field of a bar magnet.
- The strength of a solenoid’s magnetic field can be increased by inserting a magnetic material such as iron into the solenoid’s core.