# 22.9 Magnetic fields produced by currents: ampere’s law  (Page 2/12)

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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

$B=\frac{{\mu }_{0}I}{2R}\phantom{\rule{0.25em}{0ex}}\left(\text{at center of loop}\right)\text{,}$

where $R$ 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 $N$ loops; then, the field is $B={\mathrm{N\mu }}_{0}I/\left(2R\right)$ . Note that the larger the loop, the smaller the field at its center, because the current is farther away.

example ofchange of state of the body in the effectof heat
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the force that pushes upward on us. the force that opposes gravity
clifford
upthrust of air
Newton's 3rd law. the force of the ground (earth) that pushes back on gravity, keeping us on the ground instead of sinking into it.
clifford
I really need lots of questions on frictional force
Shii
I can help answering what I can
Shii
does friction also need some force to perform?
Mohit
no friction is a force just like the gravitational force
clifford
yeah but u can't apply friction anywhere else like other forces
Mohit
I don't understand that question. friction does work alongside other forces based on the situation.
clifford
eg. when walking there are two forces acting on us gravitational and frictional force. friction helps us move forward and gravity keeps us on the ground
clifford
friction is a contact force. Two surfaces are necessary for the force to work.
clifford
hope this helped
clifford
the friction force which oppose while it contact with surrounding. there are two kind of friction. slidding and rolling friction.
Neyaz
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derive the equation
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6 type of quarks
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any one can prove that 1hrpower= 746 watt
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Impulse and momentum
Fauzia
force×time and mass× velocity
vijay
Good
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oscillatory motion under a retarding force proportional to the amount of displacement from an equilibrium position
Yuri
Straight out of google, you could do that to, I suppose.
Yuri
*too
Yuri
ok
Fauzia
Oscillatory motion under a regarding force proportional to the amount of displacement from an equilibrium position
Neyaz
examples of work done by load of gravity
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You can look it up, faster and more reliable answer.
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That isn't a question to ask on a forum and I also have no idea what that is.
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Maureen
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rate of chemical reactions is proportional to concentration of reactants ...
ok thanks
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what is lenses
lenses are two types
Fauzia
concave and convex
right
Fauzia
speed of light in space
in vacuum speed of light is 3×10^8 m/s
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ok
Vikash
2.99×10^8m/s
Umair
2.8820^8m/s
Muhammed
Vikash
he is correct but we can round up in simple terms
vijay
3×10^8m/s
vijay
is it correct
Fauzia
I mean 3*10^8 m/s ok
vijay
299792458 meter per second
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3*10^8m/s
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how many Maxwell relations in thermodynamics
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how we can do prove them?
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please who has a detailed solution to the first two professional application questions under conservation of momentum
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I can help
Emeh
okay go on
True
I mean on pressure
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definition of Pressure
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it is the force per unit area of a substance.S.I unit is Pascal 1pascal is defined as 1N acting on 1m² area i.e 1pa=1N/m²
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pls explain Doppler effect
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solve this an inverted differential manometer containing oil specific gravity 0.9 and manometer reading is 400mm find the difference of pressure