# Magnetic field of a solenoid(coil)

#### Quiz

A solenoid is a coil of current carrying wire with its length larger in comparison with its diameter. When a current passes in a solenoid, what can be said about the magnetic field pattern around and inside it?

a. It is uniform.
b. It is made up of straight lines.
c. Outside it is similar to the field around a bar magnet and is uniform on the inside.
d. Outside it consists of a series of concentric circles and is made up of straight lines on the inside.

The magnetic field produced by electric current in a solenoid coil is similar to that of a bar magnet.

#### Magnetic field of a solenoid simulation

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Magnetic field of a solenoid
A solenoid is a coil of wire designed to create a strong magnetic field inside the coil. By wrapping the same wire many times around a cylinder, the magnetic field due to the wires can become quite strong. The number of turns N refers to the number of loops the solenoid has. More loops will bring about a stronger magnetic field. The formula for the field inside the solenoid is

$B=\mu_0 nI$ (n=N/L)

(N:The number of turns, L:length of solenoid, $\mu_0$ : the permeability of free space)

Fig 3-01 shows the magnetic ﬁeld lines surrounding a loosely wound solenoid. Note that the ﬁeld lines in the interior are nearly parallel to one another, are uniformly distributed, and are close together, indicating that the ﬁeld in this space is uniform and strong. The ﬁeld lines between current elements on two adjacent turns tend to cancel each other because the ﬁeld vectors from the two elements are in opposite directions. The ﬁeld at exterior points such as P is weak because the ﬁeld due to current elements on the right-hand portion of a turn tends to cancel the ﬁeld due to current elements on the left-hand portion.

Fig 3-01. The magnetic field lines for a loosely wound solenoid.

Fig 3-02 (a) Magnetic field lines for a tightly wound solenoid of finite length, arrying a teady current. The field in the interior space is nearly uniform and strong. Note that the field lines resemble those of a bar magnet, meaning that the solenoid effectively has north and south poles. (b) The magnetic field pattern of a bar magnet, displayed with small iron filings on a sheet of paper.

If the turns are closely spaced and the solenoid is of finite length, the magnetic field lines are as shown in Fig 3-02a. This field line distribution is similar to that surrounding a bar magnet (see Fig. 3-02b). Hence, one end of the solenoid behaves like the north pole of a magnet, and the opposite end behaves like the south pole. As the length of the solenoid increases, the interior field becomes more uniform and the exterior field becomes weaker. An ideal solenoid is approached when the turns are closely spaced and the length is much greater than the radius of the turns. In this case, the external field is zero, and the interior field is uniform over a great volume.

Fig 3-03 Cross-sectional view of an ideal solenoid, where the interior magnetic field is uniform and the exterior field is zero. Ampère’s law applied to the red dashed path can be used to calculate the magnitude of the interior field.