The magnetic field is a vector quantity, so the Biot-Savart law can also be written in vector form. So, if the vector notation of the current element is for in the direction of the current flowing in the conductor and vector of the distant point, then the magnetic field at that point can be written by the Biot-Savart law in vector form as If a current flows in a circular loop, then a magnetic field according to the Biot-Savart law is generated by it, So the direction of the magnetic field in the circular loop is determined using Fleming`s right thumb rule and states that „roll your finger with your right hand in the direction of the current in a circular loop, and then the direction of the thumb gives you the direction of the magnetic field in a circular loop.“ Thus, if the current flows counterclockwise, the direction of the magnetic field will be outside the plane of the loop, while clockwise, the direction of the magnetic field is in the plane of the loop. The formula of the Biot-Savart law indicates the relationship between the magnetic fields due to the current-carrying conductor at a distance from each other. The first formula of this article explains it. where μ0 is known as free space permeability. This is the mathematical formula of the Biot-Savart law. The Biot-Savart law is simply the calculation of the magnetic field based on a conductor living at a distant point in the driver`s space and the Biot-Savart law in vector form is written and calculated because the intensity of the electric field cannot be calculated using the Biot-Savart law. It is used to calculate the strength of the magnetic field. This is also used to measure flux density and permeability with the formula There is also a 2D version of the Biot-Savart equation that is used when the sources are invariant in one direction. In general, the current should not only flow in a plane perpendicular to the invariant direction and is given by [doubtful – discuss] J {displaystyle mathbf {J} } (current density). The resulting formula is: Mathematically, if dl represents the small section of a long-lived conductor with a current of I and r, the distance between the conductor and the point Say P and θ is the angle between dl and are therefore, magnetic field dB at point P due to Biot Savart`s law, As the diagram shows, The formula used to calculate the magnetic field is that since the divergence of a loop is always zero, this justifies the Gaussian law for magnetism.

Next, let`s take the lock on both sides, use the formula for the loop of a loop, and again use the fact that J does not depend on r {displaystyle mathbf {r} }, and finally get the result[15] The magnetic field on the axis of a circular current loop is calculated using the Biot-Savart law and the mathematical formula to calculate the magnetic field at any point on the axis of a circular radius loop. a and the current carrying I, then the magnetic field is at a distant point P at a distance of x, as shown in the diagram, given by This is a limit case of the formula for vortex segments of finite length (similar to a finite wire): The formulations given above work well if the current can be approximated as flowing through an infinitely narrow wire. If the conductor has a certain thickness, the correct formulation of the Biot-Savart law (always in SI units) is as follows: The Biot-Savart law states that „the magnetic field due to a conductor living at a point of distance is inversely proportional to the square of the distance between the conductor and the point, and the magnetic field is directly proportional to the length of the conductor, the current flows through the conductor.“ This is called the declaration of the Biot Savart law. In a non-magnetostatic situation, the biot-Savart law ceases to be true (it is replaced by Jefimenko`s equations), while the Gaussian law for magnetism and the Maxwell-Ampere law are always true. The Biot-Savart law can also be used in the calculation of magnetic reactions at the atomic or molecular level, for example: chemical shields or magnetic susceptibility, provided that the current density can be obtained from a calculation or theory of quantum mechanics. It is also very natural to think that the density of the magnetic field at this point P is inversely proportional to the square of the right distance from the point P to the center of dl because of this infinitesimal length dl of the wire. Mathematically, we can write this as follows: Consider a long wire carrying a current I, and also consider a point p in space. The thread is shown in red in the image below. Let us also consider an infinitely small length of the wire dl at a distance r from the point P, as shown. Here r is a distance vector that makes an angle θ with the direction of the current in the infinitesimal part of the wire. An example used in the design of the Helmholtz coil, magnets and propulsion of the Magsail spacecraft is the magnetic field at a distance x {displaystyle x} along the midline (cl), chosen as the x-axis of a loop of radius R {displaystyle R} carrying a current I {displaystyle I} as follows: In Maxwell`s 1861 paper „On Physical Lines of Force“ [14] The strength of the magnetic field H was directly equated with pure vorticity (spin), while B was a weighted vorticity weighted according to the density of the cyclone. Maxwell considered the magnetic permeability μ as a measure of the density of the cyclone.

Hence the relationship, first the Biot-Savart law was discovered experimentally, then this law was theoretically derived in different ways. In The Feynman Lectures on Physics, the similarity of the expressions of the electric potential outside the static distribution of charges and the magnetic vector potential outside the system of continuously distributed currents is first emphasized, and then the magnetic field is calculated by the curvature of the vector potential. [16] Another approach involves a general solution of the inhomogeneous wave equation for the vector potential at constant currents. [17] The magnetic field can also be calculated as a result of lorentz transformations for the electromagnetic force acting from one charged particle to another. [18] Two other ways of deriving the Biot-Savart law are: 1) the Lorentz transformation of the electromagnetic tensor components from a moving reference system, in which there is only one electric field of a certain charge distribution, into a stationary reference system in which these charges move. and (2) the use of the delayed potentials method. The magnetic field on the axis of a circular current loop is calculated as mentioned in the article and can be used to find the magnetic field of the circular loop in the center The magnetic field in the middle of a circular coil is given as the permeability of free space, the radius of the coil and the current through the coil. It is clearly defined in the above article Ans: The radius of the semicircular piece of wire = 0.20 m Therefore, the magnetic field in the middle of a circular coil The term for magnetic field B is a distance r of a long straight wire with the current I isB = μ0I / 2πr θ, where θ is a unit vector pointing in a circle around the wire.

That is, the value of the magnetic field B at a near point is directly proportional to the value of current I and inversely proportional to the vertical distance r from the wire at the given point. (Compare Ampere`s law.) The Biot-Savart law is an equation that indicates the magnetic field generated by a living segment. This segment is used as a vector size, called a current element.