31.9 Magnetic Field of a Solenoid
Asolenoidis a long coil of wire. Just as a parallel-plate capacitor gives a nearly uniform electric field between
the plates of the capacitor, a solenoid gives a nearly uniform magnetic field inside the coils (Fig. 31.2). Using
the Biot-Savart law, the magetic field in the region inside the solenoid is given by
BD 0 nI; (31.9)wherenis the number of turns per unit length in the solenoid, andIis the current in the wire.
The direction of the magnetic field inside the solenoid may be given by another right-hand rule: if you
curl the fingers of your right hand in the direction of the current, then the thumb of your right hand points in
the direction of the magnetic field inside the solenoid.
Figure 31.2: Magnetic field due to a solenoid. The solenoid is seen in cross section; current flows out of the
page for the wires at the top of the figure, and into the page for wires at the bottom. (©GNU-FDL, Wikimedia
Commons [11].)
31.10 Magnetic Field of a Loop or Coil of Wire
As discussed earlier, a magnetic dipole can be created by a bar magnet—but it can also be created by a coil
of wire. Given a coil ofNturns of wire carrying a currentI, the magnetic dipole moment of the coil can be
shown to be
mDNIAnO; (31.10)whereAis the cross-sectional area of the coil, andnOis a unit normal vector, pointing perpendicular to the
plane of the coil. The direction ofnOis given by yet another right-hand rule: if the fingers of your right hand
curl in the direction of the current, then the thumb of your right hand points in the direction ofnO(and therefore
also in the direction of the magnetic momentm).
31.11 Torque on a Magnetic Dipole in a Magnetic Field
Suppose we put a magnetic dipolemin a magnetic fieldB. (The magnetic dipole could be due to a bar
magnet, coil of wire, etc.) Then the magnetic field will exert a torqueon the dipole, equal to
DmB: (31.11)