L

SY

Z

Z

Y

ExerciseDraw the vector MAGNETICFIELD at the different points P,S, and L, respectively.

Magnetic field produced by a moving point charge

q

It aims from the charge q to the point P where we want to evaluate the magnetic field

vector position (m)

Magnetic field The unit is Tesla (T)

q

velocity (m/s)

electrical charge (Coulomb)

Magnetic field at point P,

P

P

Andres La Rosa Lecture Notes Portland State University PH-212

q

Magnetic field produced by a current

But notice,

P

P

Strategy: Divide the wire into small sections of length Δl

0P

P

Δ z

Example: Magnetic field produce by a current that flows along a straight wire

We want to evaluate the magnetic field at a point "P' located at a distance "R" from the wire

For the case of an infinitely long wire:

Contribution to theMAGNETIC FIELD at Pfrom just one currentsegment Δ z

Z

I Δ z

I

Z

Δ z

P

Q

P

BP = BQ

I

I

Lateral View

Lateral View

Infinitely long wire:

I

Magnetic field line

Question:

Question: What is the magnetic field at the point P caused by the segment AB that carries a current I ?

Question: What is the contribution to the magnetic field at P from the finite wire segment AB of length L ?

L

L/2

L/2

P

T

A Z

YX

b

a

T

Z

YX

0

I

A

I P

Exercise: Calculate the magnetic field at the points "G", "H", and "K" produced by the 2-meter wire that carries a current I = 0.5 Amps.

T

A

L=2m

ZYX

G

H

K

Force between two parallel currents

I1

wire-2

We are assuming the wires are infinitely long

- The magnetic field B1 produced by the current I1 at the site 2 is,

Magnetic field affecting the current I2

- A segment L of wire-2 is immersed in a magnetic field B1 . So the wire will experience a force,

?

B1

. . . .

. . . .

. . . .

. . . .I2I1

X

Y

Y

B1

The magnetic dipole moment

Magnetic potential energy of a dipole immersed in an external magnetic field

As usual, the potential energy of the dipole will be given with respect to a configuration reference

The torque τ makes the dipole μ to have a tendency to be aligned along the external magnetic field.

How much external work is needed to take the loop from the configuration-1 to the configuration-2?

Example

μ = N i A = 20 (0.1 Amp) (10-1m ) ( 5x10-2m )

= - 10-2 A-m2 =

B = 0.5 T

Y

Z

X

= = =

Definition of the unit current: The Ampere

Example

Along the segment BC the magnetic field produced by the 30 Amp wire is constant.

Also, along the segment DA the magnetic field produced by the 30 Amp wire is constant. For these two cases, it is convenient to use the expression,

Along the segment AB the magnetic field produced by the 30 Amp wire varies with position. Hence, in order to calculate te force on that segment of the loop, it is better to use,

30 Amp

C

DA

B

. . . .

. . . .

. . . .

. . . . 30 Amp

x x x x x x x

20 Amp

Calculate the net force acting on the loop that carries a 20 Amp currrent

B

x x x x x x x

. . . .

. . . .

A

A

B

X

X

Z

Example

Solution

P K L

KL is a semi-circle of radius "R" What is the magnetic field at point "P"?

Contribution to the magnetic field at P from the section (- � to K)? Contribution to the magnetic field at P from the section (L to � )? Contribution to the magnetic field at P from the semicircle KL?

90 degrees. Inside the plane of the

figure.

X Y

M

Magnitude of the magnetic field at point P

xx

x

x

xxx

xxx

xx

x .... .

. ..

. ..

BB

Exercise: Sketch the magnetic field of a circular coil of radius R carrying a current I.

.

.. . .

ZZ

YY

X

X

BB

Z

Question: In the figure above, where is the magnitude of the magnetic field higher, at point P or at point Q?

Notation: = # of turns per unit length