Lecture 9 *Definition and properties of magnetic field. *Differences between electric and magnetic force. *Magnetic flux.

Magnetism Recall how there are two kinds of electrical charge (+ and -), and likes repel, opposites attract. Similarly, there are two kinds of magnetic poles (north and south), and like poles repel, opposites attract. S N S N S N S N Repel Attract S N S N S N RepelAttract S N

Definition and Properties of the Magnetic Field *A magnetic field vector at some point in space is defined as a magnetic force that would be exerted on a test object. *A test object is taken to be charged particle moving with a velocity. * Experiments on the motion of various charged particles moving in a magnetic field give the following results:

1-The magnetic force is proportional to the charge (q) and speed (v) of the particle. 2-The magnitude and the direction of the magnetic force depend on the velocity of the particle and on the magnitude and direction of the magnetic field. 3-When a charged particle moves in a direction parallel to the magnetic field vector, the magnetic force on the charge is zero. 4-When the velocity vector make an angle θ with the magnetic field, the magnetic force acts in a direction perpendicular to both and, that is perpendicular to the plane formed by and,see figure (85a)

5-The magnetic force on a positive charge is in the direction opposite the direction of the force on the negative charge moving in the same direction.figure-85b 6-If the velocity vector makes an angle θ with the magnetic field, the magnitude of the magnetic force is proportional to sin θ.

We use the symbol B for magnetic field. Remember: magnetic field lines point away from north poles, and towards south poles. S N The SI unit* for magnetic field is the Tesla. In a bit, we’ll see how the units are related to other quantities we know about, and later in the course we’ll see an “official” definition of the units for the magnetic field. *Old unit, still sometimes used: 1 Gauss = Tesla. These units come from the magnetic force equation, which appears two slides from now.

Differences between electric and magnetic force: 1- The electric force always in the direction of the electric field, where as the magnetic force in the is perpendicular to the magnetic field. 2-The electric force acts on a charged particles independent of the particles velocity, where as the magnetic force acts on charged particle only when the particle is in motion. 3- The electric force does work in displacing a charged particle, where as the magnetic force associated with a steady magnetic field does not work when a particle is displaced.

The SI unit of the magnetic field is the weber per square meter ( )as also called tesla (T). We can defined tesla as a 1 coloumb of charge moving through a field of 1 tesla with a velocity of 1 m/s perpendicular to the field experiences a force of 1 newton: *In cgs units, the magnetic field unit is gauss(G). The gauss is related to the tesla through the conversion:

Example-1: A proton moves with a speed of,along the x-axis, enters a region with a field of magnitude 2.5T, directed at an angle to the x-axis and lying in the xy plane figure-87. Calculate the initial magnetic force of the proton??

Magnetic flux: The flux associated with a magnetic field is defined in a manner similar to that used to define the electric flux. Consider an element of area (dA) on an arbitrarily shaped surface as in figure-89), the magnetic field in this element is (B). The magnetic flux through the element is (B.dA), where dA a vector perpendicular to the surface whose magnitude equals the area (dA). Hence the total magnetic flux through the surface is given by:

Consider the special case of a plane of area (A) and uniform field (B)which makes an angle θ with the vector (dA). The magnetic flux through the plane in this case is given by:

If the magnetic field lies in the plane as in figure (90a) then and the flux is zero. If the field is perpendicular to the plane as in figure (90b), and the flux is (BA) ( the maximum value). Since (B) has unit of or Tesla (T), the unit of flux is the weber (Wb), where: