# Magnetic Fields due to a Solenoid

A solenoid is made out of a current-carrying wire which is coiled into a series of turns (with the turns preferably as close together as possible). The magnetic field due to a straight length of wire is shown in Figure 1 - the field circles the wire and its magnitude (or strength) decreases with radial distance from the wire.

Figure 1: Magnetic field due to a straight wire

Figure 2: Magnetic field in a solenoid

_{o}.

This gives the field in the * centre * of the solenoid.

Figure 3: Using Ampere's law to calculate Bo

*B*, i.e., for a sinusoidally varying current See Figure 4. |B

_{o}_{o}| = µ

_{o}i

_{o}N/L is the amplitude (maximum value) of the field. You can also refer to an "average" value of |B

_{o}| called, the root-mean-square (RMS) value. B

_{RMS}= |B

_{o}|/sqrt(2).

Figure 4: Time-variation of the magnetic field in the solenoid, also showing
*B _{RMS}*.

*B*at a position

*z*along the axis of the solenoid is given by

Biot-Savart Law

where R = radius of the loop. The 3rd equation shows B as a function of z when z >> R. Note that B decreases rapidly as z increases.

Figure 5: variation of B along the z-axis