Magnetism General Physics Instructor: Xiao, Yong ( 肖湧 ) ， Wang Kai( 王凯 ) TA: Li, Yueyan...

Magnetism

General Physics

Instructor: Xiao, Yong (肖湧 )，Wang Kai(王凯 )TA: Li, Yueyan （李跃岩）

Recitation TA: Zhai, Chenyu（翟宸宇）

Magnets and Magnetic Fields• The history of magnetism begins thousands of years

ago. In a region of Asia Minor known as Magnesia, rocks were found that could attract each other. These rocks were called "magnets" after their place of discovery.

Magnets and Magnetic Fields• Any magnet, whether it is in the shape of a bar or a

horseshoe, has two ends or faces, called poles, which is where the magnetic effect is strongest.

• A compass needle is simply a bar magnetwhich is supported at its center of gravity so that it can rotate freely. The pole of a freely suspended magnet that points toward geographic north is called the north pole of the magnet. The other pole points toward the south and is called the south pole.

Magnets and Magnetic Fields• When two magnets are brought near one another,

each exerts a force on the other. The force can be either attractive or repulsive.

• If the north pole of one bar magnetis brought near the north pole of asecond magnet, or the south pole withthe south pole, the force is repulsive. • When a north pole is brought near the south pole of

another magnet, the force is attractive.

Magnets and Magnetic Fields• We have all observed a magnet attract paper clips,

nails, and other objects made of iron. Only iron and a few other materials, such as cobalt, nickel, gadolinium, and some of their oxides and alloys, show strong magnetic effects. They are said to be ferromagnetic.

Magnets and Magnetic Fields• In the last course, we used the concept of an electric

field surrounding an electric charge. In a similar way, we can picture a magnetic field surrounding a magnet.

• Just as we drew electric field lines, we can also draw magnetic field lines.

Electric Currents Produce Magnetic Fields

• But in 1820, Hans Christian Oersted (1777-1851) found that when a compass needle is placed near a wire, the needle deflects as soon as the two ends of the wire are connected to the terminals of a battery and the wire carries an electric current.

• As we have seen, a compass needle is • deflected by a magnetic field. So • Oersted's experiment showed that • an electric current produces a • magnetic field.

Force on an Electric Current in a Magnetic Field• Suppose a straight wire is placed in the magnetic field

between the poles of a horseshoe magnet as shown in the figure.

• Experiments show that the direction of the force is always perpendicular to the direction of the current and the magnetic field, B.

Force on an Electric Current in a Magnetic Field• The direction of the force is given byright-hand rule.• Orient your right hand until your outstretched fingers can point in the direction of the conventional current I, and when you bend your fingers they point in the direction of the magnetic field lines, B. Then your outstretched thumb will point in the direction of the force F on the wire.

Force on an Electric Current in a Magnetic Field• So the force takes the form of:

• Where the l a unit vector towards the direction of the current. The SI unit for magnetic field B is the tesla (T). We can see that .

• If B is not uniform, or if the wire does not everywhere make the same angle with B, then the equation can be written more generally as:

Force on an Electric Current in a Magnetic Field• Example:A wire carrying a 30A current has a length at an angle with the magnetic field which is uniform at 0.90 T. Calculate the magnitude of the force on the wire.

The force:

Force on an Electric Charge Moving in a Magnetic Field• We have seen that a current experiences a force when

placed in a magnetic field. Since a current in a wire consists of moving electric charges, we might expect that freely moving charged particles would also experience a force when passing through a magnetic field.

• If N such particles of charge q pass by a given point in time t, they constitute a current . Then the force on these N particles is, .

Force on an Electric Charge Moving in a Magnetic Field• So the force on one of the N particle is:

• Notice that the direction of the acceleration of the particle is always perpendicular to the velocity. So the velocity won’t change its magnitude, but direction, which is circular motion.

Force on an Electric Charge Moving in a Magnetic Field• Example:An electron travels at in a plane perpendicular to a uniform 0.01T magnetic field. Describe its path quantitatively.

The Newton’s law:

Magnetic Dipole Moment• Example:• Calculate the torque of a square current loop with current I and aera l2, in the uniform magnetic field B.

• When the current loop turn a angle

Magnetic Dipole Moment• We find that the torque is always proportional to the area of

the coil. We define the magnetic dipole moment of the coil:

• where the direction of (and therefore of ) is perpendicular to the plane of the coil.

• If the coil consists of N loops of wire. The current is then NI, so the magnetic dipole becomes:

• The torque then takes the form of:

Magnetic Dipole Moment• Similar to the electric dipole we can define the

potential energy as:

• If we choose at , then the potential energy is:

Homework• Force on an Electric Current in a M

agnetic FieldP727/1,2,8

• Force on an Electric Charge Moving in a Magnetic FieldP727/13,21,22

• Magnetic Dipole MomentP729/35