Ampere circuital law

from biot-savart law , what I learnt was dB is perpendicular to dl and distance r , because there was a cross product dl x r . now i can integrate all dB to B and if i am carrying out the dot product of B and dl ( which were perpendicular to each other ) should mean that they should be giving me a ZERO?? Have I gone wrong in the application of direction ? pls help when you take dot products of vectors their magnitude can be written as the multiplication of both the vectors multiplied by the cosine of the angle between them, for cross products it is sine, try looking up stuff about vectors on khan academy to get a more in depth understanding of why that happens coulomb's law helps us calculate electric field due to point charges and similarly in magnetism bo sawar law helps us calculate magnetic fields due to point current elements but we've also explored gauss's law which helps us calculate electric fields in symmetric situations and we've seen that one can be obtained from the other they are equivalent and so now the question is do we have something similar in magnetism something that can help us calculate magnetic fields for symmetric situations the answer is yes we have something called ampere's circuital law and in this video we're going to ask mr ampere to help us understand his law so mr amp here what's your law tell us ampere says let's take an example imagine we have three wires that carry some current i1 i2 i3 now ampere says draw a closed loop and i ask what do y...

Ampere’s Circuital Law What is stated by Ampere’s Circuital Law? The formula for this is a closed loop integral. The integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium. Line integral to the magnetic field of the coil = μ o times the current passing through it. It is mathematically expressed as ∫ B.dl = μ o I Here μ o = permeability of free space = 4 π × 10 -15 N/ A 2 and ∫ B.dl = line integral of B around a closed path. Browse more Topics under Moving Charges And Magnetism • • • • • • Proof of Ampere’s Circuital Law Case 1: Regular Coil Consider a regular coil, carrying some current I. Let us assume a small element dl on the loop. ∫B dl = ∫B dl cos θ Here, θ is the small angle with the magnetic field. The magnetic field will be around the conductor so we can assume, θ = 0° We know that, due to a long current-carrying wire, the magnitude of the magnetic field at point P at a perpendicular distance ‘r’ from the conductor is given by, B = \( \frac \)∫dθ 1 = μ oi ∫ B.dl = μ oi So whether the coil is a regular coil or an irregular coil, the ampere’s circuital law holds true for all. Amperian Loop Ampere’s circuit law uses the Amperian loop to find the magnetic field in a region. The Amperian loop is one such that at each point of the loop, either: • B is tangential to the loop and is a non zero constant • or B is normal to the loop, or • B vanishes where Bis the induced mag...

Ampere’s circuital law states that the line integral of magnetic field intensity about any closed path is exactly equal to the direct current enclosed by that path. In the figure below, the integral of H about closed paths a and b gives the total current I, while the integral over path c gives only that portion of the James Clerk Maxwell had derived that ampere’s circuital law. It alternatively says, the integral of magnetic field intensity (H) along an imaginary closed path is equal to the current enclosed by the path. In another way we can define Ampere’s Circuital Law as the relationship between the current and the magnetic field created by the current. This law says, the integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium. Ampere’s Circuital Law applied to long straight wires The value of the magnetic field near a long straight wire is directly to proportional to the current in the wire. The Therefore we get two equations i.e. B α I and B α 1/r In order to make this an equation multiply to the proportionality constant. B= kI/r & K = μ o/2π where μ o = 4π x 10 -7 T . m/A Now we shall get B= μ oI/2πr and the most general form is B= μ oI / l Note that it really isn’t the distance from the wire, but the circumference of the circle that the magnetic field circumvents. Ampere’s Circuital Law and Solenoids A solenoid can be considered to be a set of circular loops placed s...

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)%2F12%253A_Sources_of_Magnetic_Fields%2F12.06%253A_Amperes_Law \( \newcommand\) • • • • • • • • Learning Objectives By the end of this section, you will be able to: • Explain how Ampère’s law relates the magnetic field produced by a current to the value of the current • Calculate the magnetic field from a long straight wire, either thin or thick, by Ampère’s law A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving between two different points regardless of the path chosen. Magnetic fields do not have such a property. Instead, there is a relationship between the magnetic field and its source, electric current. It is expressed in terms of the line integral of \(\vec = 0.\] The extension of this result to the general case is Ampère’s law. Ampere's Law Over an arbitrary closed path, \[\oint \vec\). If I passes through S in the same direction as your extended thumb, I is positive; if I passes through S in the direction opposite to your extended thumb, it is negative. Problem-Solving Strategy: Ampère’s Law To calculate the magnetic field created from current in wire(s), use the following s...

• العربية • Asturianu • বাংলা • Беларуская • Български • Català • Čeština • Dansk • Deutsch • Eesti • Ελληνικά • English • Español • Esperanto • Euskara • فارسی • Français • Galego • 한국어 • हिन्दी • Hrvatski • Bahasa Indonesia • Íslenska • Italiano • עברית • ქართული • Қазақша • Latviešu • Lietuvių • Magyar • Македонски • मराठी • Nederlands • नेपाली • 日本語 • Norsk bokmål • Oʻzbekcha / ўзбекча • ភាសាខ្មែរ • Polski • Português • Русский • Shqip • Slovenčina • Slovenščina • Српски / srpski • Srpskohrvatski / српскохрватски • Suomi • Svenska • Tagalog • தமிழ் • Türkçe • Українська • اردو • Tiếng Việt • 吴语 • 粵語 • 中文 The law relates magnetic fields to electric currents that produce them. A scientist can use Ampere's law to determine the magnetic field associated with a given current or current associated with a given magnetic field, if there is no time changing electric field present. In its original form, Ampère's Circuital Law relates the magnetic field to its electric current source. The law can be written in two forms, the "integral form" and the "differential form". The forms are equivalent, and related by the B or H magnetic fields. Again, the two forms are equivalent (see the " Ampère's circuital law is now known to be a correct law of physics in a Integral form [ | ] In • ∮ C B ⋅ d ℓ = μ 0 ∬ S J ⋅ d S To treat these situations, the contribution of Displacement current [ | ] See the main article: In In a dielectric the above contribution to displacement current is also pres...

from biot-savart law , what I learnt was dB is perpendicular to dl and distance r , because there was a cross product dl x r . now i can integrate all dB to B and if i am carrying out the dot product of B and dl ( which were perpendicular to each other ) should mean that they should be giving me a ZERO?? Have I gone wrong in the application of direction ? pls help when you take dot products of vectors their magnitude can be written as the multiplication of both the vectors multiplied by the cosine of the angle between them, for cross products it is sine, try looking up stuff about vectors on khan academy to get a more in depth understanding of why that happens coulomb's law helps us calculate electric field due to point charges and similarly in magnetism bo sawar law helps us calculate magnetic fields due to point current elements but we've also explored gauss's law which helps us calculate electric fields in symmetric situations and we've seen that one can be obtained from the other they are equivalent and so now the question is do we have something similar in magnetism something that can help us calculate magnetic fields for symmetric situations the answer is yes we have something called ampere's circuital law and in this video we're going to ask mr ampere to help us understand his law so mr amp here what's your law tell us ampere says let's take an example imagine we have three wires that carry some current i1 i2 i3 now ampere says draw a closed loop and i ask what do y...

Ampere’s Circuital Law What is stated by Ampere’s Circuital Law? The formula for this is a closed loop integral. The integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium. Line integral to the magnetic field of the coil = μ o times the current passing through it. It is mathematically expressed as ∫ B.dl = μ o I Here μ o = permeability of free space = 4 π × 10 -15 N/ A 2 and ∫ B.dl = line integral of B around a closed path. Browse more Topics under Moving Charges And Magnetism • • • • • • Proof of Ampere’s Circuital Law Case 1: Regular Coil Consider a regular coil, carrying some current I. Let us assume a small element dl on the loop. ∫B dl = ∫B dl cos θ Here, θ is the small angle with the magnetic field. The magnetic field will be around the conductor so we can assume, θ = 0° We know that, due to a long current-carrying wire, the magnitude of the magnetic field at point P at a perpendicular distance ‘r’ from the conductor is given by, B = \( \frac \)∫dθ 1 = μ oi ∫ B.dl = μ oi So whether the coil is a regular coil or an irregular coil, the ampere’s circuital law holds true for all. Amperian Loop Ampere’s circuit law uses the Amperian loop to find the magnetic field in a region. The Amperian loop is one such that at each point of the loop, either: • B is tangential to the loop and is a non zero constant • or B is normal to the loop, or • B vanishes where Bis the induced mag...

• العربية • Asturianu • বাংলা • Беларуская • Български • Català • Čeština • Dansk • Deutsch • Eesti • Ελληνικά • English • Español • Esperanto • Euskara • فارسی • Français • Galego • 한국어 • हिन्दी • Hrvatski • Bahasa Indonesia • Íslenska • Italiano • עברית • ქართული • Қазақша • Latviešu • Lietuvių • Magyar • Македонски • मराठी • Nederlands • नेपाली • 日本語 • Norsk bokmål • Oʻzbekcha / ўзбекча • ភាសាខ្មែរ • Polski • Português • Русский • Shqip • Slovenčina • Slovenščina • Српски / srpski • Srpskohrvatski / српскохрватски • Suomi • Svenska • Tagalog • தமிழ் • Türkçe • Українська • اردو • Tiếng Việt • 吴语 • 粵語 • 中文 The law relates magnetic fields to electric currents that produce them. A scientist can use Ampere's law to determine the magnetic field associated with a given current or current associated with a given magnetic field, if there is no time changing electric field present. In its original form, Ampère's Circuital Law relates the magnetic field to its electric current source. The law can be written in two forms, the "integral form" and the "differential form". The forms are equivalent, and related by the B or H magnetic fields. Again, the two forms are equivalent (see the " Ampère's circuital law is now known to be a correct law of physics in a Integral form [ | ] In • ∮ C B ⋅ d ℓ = μ 0 ∬ S J ⋅ d S To treat these situations, the contribution of Displacement current [ | ] See the main article: In In a dielectric the above contribution to displacement current is also pres...

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)%2F12%253A_Sources_of_Magnetic_Fields%2F12.06%253A_Amperes_Law \( \newcommand\) • • • • • • • • Learning Objectives By the end of this section, you will be able to: • Explain how Ampère’s law relates the magnetic field produced by a current to the value of the current • Calculate the magnetic field from a long straight wire, either thin or thick, by Ampère’s law A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving between two different points regardless of the path chosen. Magnetic fields do not have such a property. Instead, there is a relationship between the magnetic field and its source, electric current. It is expressed in terms of the line integral of \(\vec = 0.\] The extension of this result to the general case is Ampère’s law. Ampere's Law Over an arbitrary closed path, \[\oint \vec\). If I passes through S in the same direction as your extended thumb, I is positive; if I passes through S in the direction opposite to your extended thumb, it is negative. Problem-Solving Strategy: Ampère’s Law To calculate the magnetic field created from current in wire(s), use the following s...

Ampere’s circuital law states that the line integral of magnetic field intensity about any closed path is exactly equal to the direct current enclosed by that path. In the figure below, the integral of H about closed paths a and b gives the total current I, while the integral over path c gives only that portion of the James Clerk Maxwell had derived that ampere’s circuital law. It alternatively says, the integral of magnetic field intensity (H) along an imaginary closed path is equal to the current enclosed by the path. In another way we can define Ampere’s Circuital Law as the relationship between the current and the magnetic field created by the current. This law says, the integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium. Ampere’s Circuital Law applied to long straight wires The value of the magnetic field near a long straight wire is directly to proportional to the current in the wire. The Therefore we get two equations i.e. B α I and B α 1/r In order to make this an equation multiply to the proportionality constant. B= kI/r & K = μ o/2π where μ o = 4π x 10 -7 T . m/A Now we shall get B= μ oI/2πr and the most general form is B= μ oI / l Note that it really isn’t the distance from the wire, but the circumference of the circle that the magnetic field circumvents. Ampere’s Circuital Law and Solenoids A solenoid can be considered to be a set of circular loops placed s...