When a current-carrying loop is placed in a magnetic field, the loop tends to rotate such that its normal becomes aligned with the magnetic field.

The net torque on the loop is given by  = IAB sin . I is the current in amps, A is the area of the loop, B is the strength of the magnetic field,  is the angle between the normal to the plane of the loop and the direction of the magnetic field.

If the wire is wrapped so as to contain a number of loops N, the equation becomes:  = NIAB sin .

The torque depends on: 1) the shape and size of the coil and the current (NIA), 2) the magnitude B of the magnetic field, and 3) the orientation of the normal to the coil to the direction of the magnetic field (sin  ).

NIA is known as the magnetic moment of the coil with the units amperemeter 2. The greater the magnetic moment, the greater the torque experienced when the coil is placed in a magnetic field.

Ex. 6 - A coil of wire has an area of 2.0 x m 2, consists of 100 loops, and contains a current of A. The coil is placed in a uniform magnetic field of magnitude 0.15 T. (a) Determine the magnetic moment of the coil. (b) Find the maximum torque that the magnetic field can exert on the coil.

A dc motor is set up in such a way that the direction of the current produces the proper torque due to the attraction and repulsion of permanent magnets. The permanent magnets are stationary, so the direction of the current must change to keep the loop rotating.

A current-carrying wire can experience a magnetic force when placed in a magnetic field. A current-carrying wire also produces a magnetic field. This phenomenon was discovered by Hans Christian Oersted.

Oersted’s discovery linked the movement of charges to the production of a magnetic field, and marked the birth of the study of electromagnetism.

When current is passing through a wire the magnetic field lines are cricles centered on the wire. The direction of the magnetic field is found using Right-Hand Rule No. 2 (RHR-2).

Right-Hand Rule No. 2 - When the fingers of the right hand are curled, and the thumb points in the direction of the current I, the tips of the fingers point in the direction of the magnetic field B.

The strength of the magnetic field is given by: B = µ 0 I/2πr. µ 0 is the permeability of free space, µ 0 = 4π x Tm/A I is the current, r is the radial distance from the wire.

Ex. 8 - A long, straight wire carries a current of I = 3.0 A. A particle of charge q 0 = +6.5 x C is moving parallel to the wire at a distance of r = m; the speed of the particle is v = 280 m/s. Determine the magnitude and direction of the magnetic force exerted on the moving charge by the current in the wire.

Ex. 9 - Two straight wires run parallel. The wires are separated by a distance of r = m and carry currents of I 1 = 15 A and I 2 = 7.0 A. Find the magnitude and direction of the force that the magnetic field of wire 1 applies to a 1.5-m length of wire 2 when the currents are (a) in opposite directions and (b) in the same direction.

Ex A straight wire carries a current I 1 and a rectangular coil carries a a current I 2. The wire and the coil lie in the same plane, with the wire parallel to the long sides of the rectangle. Is the coil attracted to or repelled from the wire?

At the center of a current- carrying loop of radius R, the magnetic field is perpendicular to the plane of the loop and has the value B = µ 0 I/(2R). If the loop consists of N turns of wire, the field is N times greater than that of a single loop.

At the center of a circular, current-carrying loop: B = Nµ 0 I/(2R). RHR-2 enables us to find the direction of the magnetic field at the center of the loop.

Ex A long, straight wire carries a current of I 1 = 8.0 A. A circular loop of wire lies immediately to the right of the straight wire. The loop has a radius of R = m and carries a current of I 2 = 2.0 A. Assuming that the thickness of the wires is negligible, find the magnitude and direction of the net magnetic field at the center C of the loop.

A coil of current-carrying wire produces a magnetic field exactly as if a bar magnet were present at the center of the loop. Changing the direction of flow of the current changes the polarity of the magnetic field. Two adjacent loops can attract or repel each other depending on the direction of flow of the current.

A solenoid is a long coil of wire. If the coils are tightly packed and the solenoid is long compared to its diameter, the magnetic field inside the solenoid and away from its ends is nearly constant in magnitude and directed parallel to the axis.

The magnitude of the magnetic field in a solenoid is B = µ 0 nI. n is the number of turns per unit length of the solenoid (turns/meter) and I is the current.

If the length of the solenoid is much greater than its diameter, the magnetic field is nearly zero outside the solenoid. A solenoid is often called an electromagnet. They are used in MRI’s cathode ray tubes, power door locks, etc.

The magnetic fields produced by long straight wires, wire loops, and solenoids are distinctly different.

Although different, each field can be obtained from a general law: Ampere’s Law.

Ampere’s law is valid for a wire of any shape. For any current geometry that produces a magnetic field that does not change in time, ∑B ll ∆ l = µ 0 I.

∑B ll ∆ l = µ0I ∆ l is a small segment of length along a closed path of arbitrary shape around the current, B ll is the component of the magnetic field parallel to ∆ l, I is the net current, ∑ indicates the sum of all B ll ∆ l

The magnetic field around a bar magnet is due to the motion of charges, but not the flow of electricity. It is due to the motion of the electrons themselves. The orbit of the electron around the nucleus is like an atom-sized loop of current, in addition the electron spin also produces a magnetic field.

In most substances, the total effect of all the electrons cancels out. But in ferromagnetic materials it does not cancel out for groups of 1016 to 1018 neighboring atoms. Instead some of the electron spins are naturally aligned forming a small (0.01 to 0.1 mm) highly magnetized region called a magnetic domain.

Each domain behaves as a small magnet. Common ferromagnetic materials: iron, nickel, cobalt, chromium dioxide, and alnico.

In ferromagnetic materials the domains may be arranged randomly, so it displays little magnetism. When placed in an external magnetic field, the unmagnetized material can receive an “induced” magnetism.

The domains that are parallel to the field can be caused to grow by adding electrons to their domain. Some domains may even reorient to be aligned with the magnetic field.

Induced magnetism causes the previously nonmagnetic material to behave as a magnet. A weak field can produce an induced field which is 100 to 1000 times stronger than the external field.

In nonferromagnetic materials, like aluminum and copper, domains are not formed, so magnetism cannot be induced.

The ampere is now defined as the amount of electric current in each of two long, parallel wires that gives rise to a magnetic force per unit length of 2 x N/m on each wire when the wires are separated by one meter. (previously I = ∆q/∆t)

One coulomb is now similarly defined as the quantity of electrical charge that passes a given point in one second when the current is one ampere, or 1 C = 1As.