Sources of Magnetic Field

Physics 72 Bareza AY 15-16 1st sem 1

C


Magnetic forces arise in two stages:

Fundamental nature

of Magnetism

Interaction of moving

electric charges

1. Moving charge or a collection of moving charges

produces a magnetic field.

2. Current or moving charge responds to this

magnetic field and so experiences a magnetic

force.

Chapter 28Sources of Magnetic Field

28-1 Magnetic Field of a Moving Charge

28-2 Magnetic Field of a Current Element

28-3 Magnetic Field of a Straight Current-Carrying Conductor

28-4 Force Between Parallel Conductors

28-5 Magnetic Field of a Circular Current Loop

28-6 Amperes Law

28-7 Applications of Amperes Law


Objective

Evaluate the magnetic field vector at a given point in space due to a moving point charge



Electric Interactions

1. A distribution of electric charge at rest creates an electric field

in the surrounding space.

2. The electric field exerts a force on any other charge q

that is present in the field.

Magnetic Interactions

1. A moving charge or a current creates a magnetic field in the

surrounding space (in addition to its electric field).

2. The magnetic field exerts a force on any other moving

charge or current that is present in the field.


What is the magnetic field at point P?

Question:

+q

Field pointSource point

Point P


Magnetic Field of a Point Charge with Constant Velocity



Direction: Use RHR.


Example:

Answers: e = neg charge of electron; v = 0.100c, r = 2.00 um(a) B = k*e*v*sin(30)/r^2; out of the page(b) B = k*e*v/r^2; out of the page(c) zero


Seatwork:What is the direction of the

magnetic field at point P due

to the two moving charges?

Answer: +i or

out of the page


Example:What is the magnitude of the

magnetic field at point P due

to the two moving charges?

Answer:No B due to +3e.B due to +4e = k*(4e)*vo*(L)/[(L^2 + (2L)^2)^(3/2)]Out of the page







28-6 Amperes Law



Objective

Evaluate the magnetic field vector at a given point in space due to an infinitesimal current element




Question:


Point P


Magnetic Field of a Current Element

Biot-Savart law

Direction: Use RHR.

Magnetic Field of a Current Element


Example:


Seatwork



Point P

Biot-Savart law







28-6 Amperes Law



Objectives

Evaluate the magnetic field vector at any point in space due to a straight current-carrying conductor

Use superposition principle to calculate the magnetic field due to one or more straight wire conductors



What is the magnetic

field at point P?

Question:


At all points on a circle of radius r around a long,

straight current-carrying wire, the magnitude B is

For a long, straight, current-carrying conductor only

radius r


Three long, straight conducting wires each carry a current I

in the direction shown. What is the magnitude and direction

of the resulting magnetic field at point P?

Example:

Answer: B = (5/4)uI/4piR, upward


Seatwork:Four, long, parallel power line each carry 100-A currents. A

cross-sectional diagram of these lines is a square, 20.0 cm

on each side. What is the direction of the net magnetic

field at the center of the square?







28-6 Amperes Law



Objective

Calculate the force per unit length on a current carrying wire due to the magnetic field produced by other current-

carrying wires



The lower conductor produces a

magnetic field that, at the position of

the upper conductor, has magnitude

The magnetic force that this field

exerts on a length L of the upper

conductor is

rI

I

L


The magnetic force experienced by the segment having length L on the

upper conductor is

Magnitude:

Direction: downward

Magnitude:

Direction:

Lower conductor produces a

magnetic field in this portion.


r I

I LMagnitude:

Direction:

Upper conductor produces a

magnetic field in this portion.

The magnetic force experienced by the segment having length L on the

lower conductor is

Magnitude:

Direction: upward


r

I

I

Two long, parallel, current-carrying conductors attract if

the currents are in the same direction.

Conclusion:

Newtons 3rd law? Yes!


Two long, parallel, current-carrying conductors repelif the currents are in the opposite direction.

Two long, parallel, current-carrying conductors attract if the currents are in the same direction.

Conclusion:




Force per unit Length

Applicable for any two long, parallel, current-carrying conductors

lower conductor upper conductor


Equation to be used:

Example:


Seatwork:







28-6 Amperes Law



Objective

Evaluate the magnetic field vector at any point along the axis of a circular current loop




Question:

Apply Biot-Savart law.



Question:

(on the axis of a circular loop)

Magnitude:

Direction:

Use:


For a coil consisting of N loops, all with the

same radius a,

(on the axis of N circular loops)

At the center of the coil (x = 0):

(at the center of N circular loops)


In general:

(on the axis of a circular loop)

(on the axis of N circular loops)

What we have right now:

For N = 1:

For N > 1:


Example:Consider a circular conducting loop with radius 10 cm lying

in the yz-plane centered at the origin. It carries current I =

1.5 A directed in the counterclockwise direction as viewed

from the +x-axis.

What is the magnitude and direction

of the magnetic field at the origin?

Answers:Direction +x-axisMagnitude = uI/2R (substitute values)


Apply Biot-Savart law.

Example:







28-6 Amperes Law



Objective

Use Amperes law to calculate magnetic fields for highly symmetric current configurations



Amperes Law


Example: Answers:a: 0b: -uI1c: u(I2-I1)d: u(I2+I3-I1)


Seatwork:Which of the following statements is correct about line integral

along paths A, B and C?

A. The line integral along path A is positive.

B. The line integral along path B is positive.

C. The line integral along path C is positive.

D. The line integral along paths A and B is the

same.

E. The line integral along paths A, B and C are

the same.


Example: (a) B = uI/2pir(b) B = 0Note: if we consider regions in b

N: number of turns

L: length

n = N/L

Note:



Consider two very long solenoids S1 and S2. S1 has N

number of loops and length L while S2 has 2N number of

loops and length 2L. If these solenoids are connected in

series to an emf source, compare the relative magnitudes of

the magnetic field (BS1 and BS2) inside the two solenoids.

Example:

Equal current in S1 and S2 since they are in series. B = unI for solenoid, since they both have same current and same coil density, then B inside for both should be equal


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Sources of Magnetic Field

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