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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

definition of mass of conversion
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how many topic are in physics
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what is Linear motion
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straight line motion is called linear motion
then what
linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
your are wrong Saeedul
Linear motion is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimensions. 
what is a classical electrodynamics?
what is dynamics
dynamic is the force that stimulates change or progress within the system or process
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David Reply
if a spring is is stiffness of 950nm-1 what work will be done in extending the spring by 60mmp
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State the forms of energy
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Word : Mechanical wave Definition : The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
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a wave which require material medium for its propagation
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Samuel Reply
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SI.unit of power is.watt=j/c.but kw.and Mw are bigger.umots
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aish Reply
study of matter and its nature
The word physics comes from a Greek word Physicos which means Nature.The Knowledge of Nature. It is branch of science which deals with the matter and energy and interaction between them.
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Syafiqah Reply
because it is balanced by the inward acceleration otherwise known as centripetal acceleration
What is a wave
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Tramsmission of energy through a media
is the disturbance that carry materials as propagation from one medium to another
mistakes thanks
find the triple product of (A*B).C given that A =i + 4j, B=2i - 3j and C = i + k
Favour Reply
Practice Key Terms 9

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