<< Chapter < Page Chapter >> Page >

Magnetic field produced by a current-carrying solenoid

A solenoid    is a long coil of wire (with many turns or loops, as opposed to a flat loop). Because of its shape, the field inside a solenoid can be very uniform, and also very strong. The field just outside the coils is nearly zero. [link] shows how the field looks and how its direction is given by RHR-2.

A diagram of a solenoid. The current runs up from the battery on the left side and spirals around with the solenoid wire such that the current runs upward in the front sections of the solenoid and then down the back. An illustration of the right hand rule 2 shows the thumb pointing up in the direction of the current and the fingers curling around in the direction of the magnetic field. A length wise cutaway of the solenoid shows magnetic field lines densely packed and running from the south pole to the north pole, through the solenoid. Lines outside the solenoid are spaced much farther apart and run from the north pole out around the solenoid to the south pole.
(a) Because of its shape, the field inside a solenoid of length l size 12{l} {} is remarkably uniform in magnitude and direction, as indicated by the straight and uniformly spaced field lines. The field outside the coils is nearly zero. (b) This cutaway shows the magnetic field generated by the current in the solenoid.

The magnetic field inside of a current-carrying solenoid is very uniform in direction and magnitude. Only near the ends does it begin to weaken and change direction. The field outside has similar complexities to flat loops and bar magnets, but the magnetic field strength inside a solenoid    is simply

B = μ 0 nI ( inside a solenoid ) , size 12{B=μ rSub { size 8{0} } ital "nI"` \( "inside a solenoid" \) ,} {}

where n size 12{n} {} is the number of loops per unit length of the solenoid ( n = N / l size 12{ \( n=N/l} {} , with N size 12{N} {} being the number of loops and l size 12{l} {} the length). Note that B size 12{B} {} is the field strength anywhere in the uniform region of the interior and not just at the center. Large uniform fields spread over a large volume are possible with solenoids, as [link] implies.

Calculating field strength inside a solenoid

What is the field inside a 2.00-m-long solenoid that has 2000 loops and carries a 1600-A current?

Strategy

To find the field strength inside a solenoid, we use B = μ 0 nI size 12{B=μ rSub { size 8{0} } ital "nI"} {} . First, we note the number of loops per unit length is

n = N l = 2000 2.00 m = 1000 m 1 = 10 cm 1 . size 12{n rSup { size 8{ - 1} } = { {N} over {l} } = { {"2000"} over {2 "." "00" m} } ="1000"" m" rSup { size 8{ - 1} } ="10"" cm" rSup { size 8{ - 1} } "." } {}

Solution

Substituting known values gives

B = μ 0 nI = × 10 7 T m/A 1000 m 1 1600 A = 2 .01 T.

Discussion

This is a large field strength that could be established over a large-diameter solenoid, such as in medical uses of magnetic resonance imaging (MRI). The very large current is an indication that the fields of this strength are not easily achieved, however. Such a large current through 1000 loops squeezed into a meter’s length would produce significant heating. Higher currents can be achieved by using superconducting wires, although this is expensive. There is an upper limit to the current, since the superconducting state is disrupted by very large magnetic fields.

Got questions? Get instant answers now!

There are interesting variations of the flat coil and solenoid. For example, the toroidal coil used to confine the reactive particles in tokamaks is much like a solenoid bent into a circle. The field inside a toroid is very strong but circular. Charged particles travel in circles, following the field lines, and collide with one another, perhaps inducing fusion. But the charged particles do not cross field lines and escape the toroid. A whole range of coil shapes are used to produce all sorts of magnetic field shapes. Adding ferromagnetic materials produces greater field strengths and can have a significant effect on the shape of the field. Ferromagnetic materials tend to trap magnetic fields (the field lines bend into the ferromagnetic material, leaving weaker fields outside it) and are used as shields for devices that are adversely affected by magnetic fields, including the Earth’s magnetic field.

Phet explorations: generator

Generate electricity with a bar magnet! Discover the physics behind the phenomena by exploring magnets and how you can use them to make a bulb light.

Generator

Section summary

  • The strength of the magnetic field created by current in a long straight wire is given by
    B = μ 0 I 2 πr ( long straight wire ) ,
    where I size 12{I} {} is the current, r size 12{r} {} is the shortest distance to the wire, and the constant μ 0 = × 10 7 T m/A size 12{μ rSub { size 8{0} } =4π times "10" rSup { size 8{ - 7} } `T cdot "m/A"} {} is the permeability of free space.
  • The direction of the magnetic field created by a long straight wire is given by right hand rule 2 (RHR-2): Point the thumb of the right hand in the direction of current, and the fingers curl in the direction of the magnetic field loops created by it.
  • The magnetic field created by current following any path is the sum (or integral) of the fields due to segments along the path (magnitude and direction as for a straight wire), resulting in a general relationship between current and field known as Ampere’s law.
  • The magnetic field strength at the center of a circular loop is given by
    B = μ 0 I 2 R ( at center of loop ) , size 12{B= { {μ rSub { size 8{0} } I} over {2R} } " " \( "at center of loop" \) ,} {}
    where R size 12{R} {} is the radius of the loop. This equation becomes B = μ 0 nI / ( 2 R ) size 12{B=μ rSub { size 8{0} } ital "nI"/ \( 2R \) } {} for a flat coil of N size 12{N} {} loops. RHR-2 gives the direction of the field about the loop. A long coil is called a solenoid.
  • The magnetic field strength inside a solenoid is
    B = μ 0 nI ( inside a solenoid ) , size 12{B=μ rSub { size 8{0} } ital "nI"" " \( "inside a solenoid" \) ,} {}
    where n size 12{n} {} is the number of loops per unit length of the solenoid. The field inside is very uniform in magnitude and direction.

Conceptual questions

Make a drawing and use RHR-2 to find the direction of the magnetic field of a current loop in a motor (such as in [link] ). Then show that the direction of the torque on the loop is the same as produced by like poles repelling and unlike poles attracting.

Got questions? Get instant answers now!

Questions & Answers

how to study physic and understand
Ewa Reply
what is work
Fredrick Reply
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
AI-Robot
why is it from light to gravity
Esther Reply
difference between model and theory
Esther
Is the ship moving at a constant velocity?
Kamogelo Reply
The full note of modern physics
aluet Reply
introduction to applications of nuclear physics
aluet Reply
the explanation is not in full details
Moses Reply
I need more explanation or all about kinematics
Moses
yes
zephaniah
I need more explanation or all about nuclear physics
aluet
Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity
Muhammad Reply
yh
Isaac
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
Majok Reply
what is frontier of physics
Somto Reply
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Gufraan Reply
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
Ezekiel Reply
please explain
Samuel
what's the definition of physics
Mobolaji Reply
what is physics
Nangun Reply
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
AI-Robot
what is isotopes
Nangun Reply
nuclei having the same Z and different N s
AI-Robot
Practice Key Terms 9

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask