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Ampere’s law and others

The magnetic field of a long straight wire has more implications than you might at first suspect. Each segment of current produces a magnetic field like that of a long straight wire, and the total field of any shape current is the vector sum of the fields due to each segment. The formal statement of the direction and magnitude of the field due to each segment is called the Biot-Savart law    . Integral calculus is needed to sum the field for an arbitrary shape current. This results in a more complete law, called Ampere’s law    , which relates magnetic field and current in a general way. Ampere’s law in turn is a part of Maxwell’s equations    , which give a complete theory of all electromagnetic phenomena. Considerations of how Maxwell’s equations appear to different observers led to the modern theory of relativity, and the realization that electric and magnetic fields are different manifestations of the same thing. Most of this is beyond the scope of this text in both mathematical level, requiring calculus, and in the amount of space that can be devoted to it. But for the interested student, and particularly for those who continue in physics, engineering, or similar pursuits, delving into these matters further will reveal descriptions of nature that are elegant as well as profound. In this text, we shall keep the general features in mind, such as RHR-2 and the rules for magnetic field lines listed in Magnetic Fields and Magnetic Field Lines , while concentrating on the fields created in certain important situations.

Making connections: relativity

Hearing all we do about Einstein, we sometimes get the impression that he invented relativity out of nothing. On the contrary, one of Einstein’s motivations was to solve difficulties in knowing how different observers see magnetic and electric fields.

Magnetic field produced by a current-carrying circular loop

The magnetic field near a current-carrying loop of wire is shown in [link] . Both the direction and the magnitude of the magnetic field produced by a current-carrying loop are complex. RHR-2 can be used to give the direction of the field near the loop, but mapping with compasses and the rules about field lines given in Magnetic Fields and Magnetic Field Lines are needed for more detail. There is a simple formula for the magnetic field strength at the center of a circular loop    . It is

B = μ 0 I 2 R ( at center of loop ) , size 12{B= { {μ rSub { size 8{0} } I} over {2R} } ` \( "at center of loop" \) ,} {}

where R size 12{R} {} is the radius of the loop. This equation is very similar to that for a straight wire, but it is valid only at the center of a circular loop of wire. The similarity of the equations does indicate that similar field strength can be obtained at the center of a loop. One way to get a larger field is to have N size 12{N} {} loops; then, the field is B = 0 I / ( 2 R ) . Note that the larger the loop, the smaller the field at its center, because the current is farther away.

Figure a illustrates use of the right hand rule 2 to determine the direction of the magnetic field around a current-carrying loop. The right hand thumb points in the direction of I while the fingers curl around in the direction of B. Figure b shows the magnetic field lines circling the wire, as viewed from the side.
(a) RHR-2 gives the direction of the magnetic field inside and outside a current-carrying loop. (b) More detailed mapping with compasses or with a Hall probe completes the picture. The field is similar to that of a bar magnet.

Questions & Answers

If an object has no acceleration in an inertial reference frame, can you conclude that no forces are acting on it?
Von Reply
No unbalanced forces
Sorry, no unbalanced net force
What are the two major system units in the world
Jizel Reply
What is physical quantities
they are physical properties that can be measured or calculated
Do you mean the SI system and Imperial system? SI is used by scientists the world over (with notable exception being the USA)
Who is the father of physics
Gabriel Reply
Newton.Geliliyo and Einstein is called father of physics
Ancient - Archimedes Classical Physics - Newton Modern Physics - Einstein But each of these has built on the work of predecessors. No single personality defines physics.
Galileo Galilie must be. He was the creator of the scientific method
Galileo was no doubt inspirational, but the scientific method has existed for millennia. What Galileo did was prove the superiority of experimentation to just thinking (Aristotle's way). Again all noteworthy scientists
Newton galileo and Einstein
what is wave
Charity Reply
a wave is a distirbance that transmits energy from one place ro another within or without a medium
wave is the transfer of energy from one medium to another without the transfer of particles
wave is a disturbance which transfer energy from one medium to another without causing any permanent displacement by itself
wave is a disturbance or oscillation that travel through space and matter,accompanied by a transfer of energy
A wave is any disturbances in an elastic medium which carries energy from one point to another through a medium
what is harmonic motion
is a restoring force
a wave is a disturbance and there are trasfer energy from one medium to another and travel through any space without the trasfer of particles.
a wave is a disturbance that travels or carries energy from one point to another through a medium
A moving disturbance in the level of a body water, undulation
what is thermodynamics
Williams Reply
what is thermodynamics
thermodynamics is a heat and energy significant physics
Relating to the conversation of heat into other forms of energy
It's the science of conversion between heat and other forms of energy
Are the antimatters of Hadrons also Hadrons?!Does the same rule apply to Leptons?
Daniel Reply
yes. Hadrons are the elementary particles that take part in stong, electromagnetic and weak interactions. Infact only Hadrons are involved in Strong interactions and when an anti-particle of any hadron is produced, it would be a hadron-conservations laws. Leptons are involved in weak int and follow
what is physics
physic is a pure science that deal with behavior of matter,energy & how it related to other physical properties
Owk. But am are Art student.
Thanks a lot,Lalita
what are the differences between reflection and refraction ?
What happens when an aeroplanes window is opened at cruise altitude?
Theophilus Reply
what is the minimum speed for any object to travel in time?
Pankaj Reply
as per theory of relativity, minimum speed will be the speed of light
what is physics
Lote Reply
it is just a branch of science which deals with the reasons behind the daily activities taking place everyday in our lives. it clearly states the reason in the form of laws.
like Newton's laws , Kepler's laws etc....
physics is the study of motion or moving things. Usually the moving things are normal items like vars or planets but sometimes it's electricity or heat that moves.
physics is one of the most significant diciplines of natural science which describe the nature and its matter
I would describe it as the science that is interested in the fundamental laws of nature. For example, what is light, what is sound, what is electricity/magentism, what forces are at work on a specific body. The knowledge of the world around us makes it possible to fly, have cell phones, GPS, etc.
what happens when an aeroplane takes off?
Kofi Reply
it flies
the lift generated by the wing overcome the weight of the plane(in Newton)and a net force of upward is created
it is a direct application of Magnus effect (which helps in throwing curve balls) the wings of plane are made in such a way that the net flow of air is more below them rather than on their upper side. So when the plane accelerates, the flaps produce the upward lift when enough velocity is obtained
then due to lower pressure on upper part of wings helps producing an additional lift because air flows from areaof lower to the area of higher pressure
The engines located under the wings generate thrust .. in relation thrust is a force ... which ovwrcomes or becomes greater than the weight of the plane.. remember weight is a force Weight = m x g-2 So therefore F(thrust) becomes greater than F(weight) Even if by 1Newton the plane starts lifting o
what happens when a ship moves
What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?
Conwil Reply
If it reduces the magnitude of the velocity, the acceleration sign is the opposite compared to the velocity.
what is accerelation
John Reply
an objects tendency to speed up over time
acceleration is the change in velocity over the change in time it would be written delta-v over delta-t.
the change in velocity V over a period of time T.
Delta means "change in"...not period of
just kidding. it all works mathematically
except doesn't time really only change if the instantaneous speeds vary...?
and I assume we are all talking average acceleration
Hey shiii 😀
the rate of change of velocity is callaed acceleration
a=delta v/delta t
the rate of change in velocity with respect to time is acceleration
nana you r right
what is meant by lost volt
Hardeyyemih Reply
Lost volt. Lol. It is the electrical energy lost due to the nature or the envirommental conditions (temperature and pressure) that affect the cable across which the potential difference is measured.
What is physics?
Bedabyas Reply
physics is brance science concerned with nature and properties of matter and energy
physics is study of the natural phenomenon on the basis of certain laws and principles. it's like watching a game of chess and trying to understand its rules how it's played.
physics is study of nature and it's law
physics is a branch of science that deals with the study of matter ,properties of matter and energy
Branch of science (study) of matter, motion and energy
what is a double-slit experiment?Explain.
Daniel Reply
when you pass a wave of any kind ie sound water light ect you get an interface pattern forming on a screen behind it, where the peaks and troughs add and cancel out due to the diffraction caused by a wave traveling through the slits
double slit experiment was done by YOUNG. And it's to give out monochromatic coherent, if an incoherent wave is passing through it. And then the waves form interference fringes. The screen placed in front of the double slit is preferably a film and then in the middle where "p=0" a brighter color
is formed and then the constructive interferences occur at 0 (which is the brightest band)... then a sequence of bright band (constructive interference) and dark band (destructive interference) happens and the further from the central band the lower the intensity of bright band(constructive interfe
Practice Key Terms 9

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