Kanunadda Biot-Savart: Inganci, Tashar Farko da Ayyuka

Me kana Biot Savart Law

An Biot Savart Law ita ce ta hanyar takardun magnetic field da juna ciki ne kan electric current. Yana nuna magnetic field da tsari, yadda, girman, da kyau da karfin electric current. An sami Biot–Savart law da Ampere’s circuital law da Gauss’s theorem. Biot Savart law ita ce muhimmiyar zuwa magnetostatics, tare da wani matsayin da Coulomb’s law tana da shi a electrostatics.

Biot-Savart law an gina shi da biyu masana'antu mai fizikis na Faransanci, Jean Baptiste Biot da Felix Savart, suka gina takarda mathematika don magnetic flux density a wurin da ya ba kan current-carrying conductor, a shekarar 1820. Daga bincike da suka yi game da compass needle, waɗannan biyu masana'antu sun fi sani cewa babu current element ba da zama magnetic field a cikin duk fadinai.

Daga binciken da suka yi da abubuwan da suka bayyana, suka gina takarda mathematika, wanda yake nuna, cewa magnetic flux density, da dB, ita ce muhimmiya da tsari da dl, current I, sine of the angle and θ daga hukuma da ke current da vector joining a given point of the magnetic field and the current element and is inversely proportional to the square of the distance of the given point from the current element, r.

Biot Savart Law Statement & Derivation

An iya cewa Biot-Savart law ita ce:

Idan, k ita ce sabbin da take depenndence upon the magnetic properties of the medium and system of the units employed. A SI system of unit,

Saboda haka, an sami Biot-Savart law derivation ita ce,

Ba ni da wire mai girma da ya kula current I, kuma ba ni da wurin p a cikin space. Wire ita ce a cikin hoton da aka nuna, da lafiya. Ba ni da infinitesimal length of the wire dl a r distance away from the point P as shown. Idan, r ita ce distance-vector wanda yake da angle θ with the direction of current in the infinitesimal portion of the wire.

Idan kana iya fahimta cewa, za ku iya samun cewa magnetic field density a wurin P because of that infinitesimal length dl of the wire ita ce muhimmiya da current carried by this portion of the wire.

Saboda current through that infinitesimal length of wire ita ce mafi yawan current carried by the whole wire itself, za a iya rubuta,

Ita ce da maƙasance a fahimtar cewa magnetic field density at that point P because of that infinitesimal length dl of wire ita ce inversely proportional to the square of the straight distance from point P to the center of dl. Mathematically we can write this as,

Kafin, magnetic field density at that point P because of that infinitesimal portion of the wire ita ce muhimmiya da actual length of the infinitesimal length dl of wire.

Idan θ ita ce angle between distance vector r and direction of current through this infinitesimal portion of the wire, component of dl directly facing perpendicular to the point P is dlsinθ,

Na gode, daga wannan uku bayanan, za a iya rubuta,

Wannan ita ce form basic of Biot Savart’s Law

Na gode, putting the value of constant k (which we have already introduced at the beginning of this article) in the above expression, we get

Hakan, μ0 used in the expression of constant k ita ce absolute permeability of air or vacuum and its value is 4π10-7 Wb/ A-m in the SI system of units. μr of the expression of constant k ita ce relative permeability of the medium.

Na gode, flux density(B) at the point P because of the total length of the current-carrying