ElectromagnetismLecture#15

Instructor:Muhammad Mateen Yaqoob

Magnetic Fields

In 1269 a Frenchman named Pierre de Maricourt found that directions of a needle near a spherical natural magnet formed lines that encircled sphere and passed through two points diametrically opposite each other, which he called poles of magnet.

Subsequent experiments showed that every magnet, regardless of its shape, has two poles, called north (N) and south (S) poles, that exert forces on other magnetic poles similar to way that electric charges exert forces on one another.

Poles received their names because of way a magnet, such as that in a compass, behaves in presence of Earth’s magnetic field.

Mateen Yaqoob Department of Computer Science

Magnetic Fields

Although force between two magnetic poles is otherwise similar to force between two electric charges, electric charges can be isolated (witness electron and proton) whereas a single magnetic pole has never been isolated. That is, magnetic poles are always found in pairs.

Mateen Yaqoob Department of Computer Science

Magnetic Fields and Forces

In our study of electricity, we described interactions between charged objects in terms of electric fields.

In addition to containing an electric field, region of space surrounding any moving electric charge also contains a magnetic field.

A magnetic field also surrounds a magnetic substance making up a permanent magnet.

Symbol B has been used to represent a magnetic field. Direction of magnetic field B at any location is direction in which a compass needle points at that location.

Mateen Yaqoob Department of Computer Science

Magnetic Fields and Forces

We can represent magnetic field by means of drawings with magnetic field lines.

Mateen Yaqoob Department of Computer Science

Defining a magnetic field

We can define a magnetic field B at some point in space in terms of the magnetic force FB that field exerts on a charged particle moving with a velocity v, which we call test object.

Experiments on various charged particles moving in a magnetic field give following results:

1. Magnitude FB of magnetic force exerted on particle is proportional to charge q and to speed v of particle.

2. Magnitude and direction of FB depend on velocity of particle and on magnitude and direction of magnetic field B.

3. When a charged particle moves parallel to magnetic field vector, magnetic force acting on particle is zero.

Mateen Yaqoob Department of Computer Science

Defining a magnetic field

4. When particle’s velocity vector makes any angle θ (non-zero) with magnetic field, magnetic force acts in a direction perpendicular to both v and B; that is, FB is perpendicular to plane formed by v and B.

5. Magnetic force exerted on a positive charge is in direction opposite direction of magnetic force exerted on a negative charge moving in same direction.

6. Magnitude of magnetic force exerted on moving particle is proportional to sinθ, where θ is angle particle’s velocity vector makes with direction of B.

Mateen Yaqoob Department of Computer Science

Defining a magnetic field

We can summarize these observations by writing magnetic force in form:

SI unit of magnetic field is newton per coulomb-meter per second, which is called Tesla (T)

A non-SI magnetic-field unit in common use, called gauss (G), is related to tesla through conversion 1T= 104 G

Mateen Yaqoob Department of Computer Science

Magnetic Force Acting on a Current-Carrying Conductor

If a magnetic force is exerted on a single charged particle when particle moves through a magnetic field, it should not surprise you that a current-carrying wire also experiences a force when placed in a magnetic field.

This follows from fact that current is a collection of many charged particles in motion; hence, resultant force exerted by field on wire is vector sum of individual forces exerted on all charged particles making up current.

Force exerted on particles is transmitted to wire when particles collide with atoms making up wire.

Mateen Yaqoob Department of Computer Science

Magnetic Force Acting on a Current-Carrying Conductor

Let us quantify by considering a straight segment of wire of length L and cross-sectional area A, carrying a current I in a uniform magnetic field B

Magnetic force exerted on a charge q moving with a drift velocity Vd is qVdxB. To find total force acting on the wire, we multiply the force qVdxB exerted on one charge by number of charges in the segment.

Because volume of segment is AL, number of charges in segment is nAL, where n is number of charges per unit volume. Hence, total magnetic force on wire of length L is

Mateen Yaqoob Department of Computer Science