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The Biot-Savart Law describes the magnetic fields due to a steady current. It is a simplification of the more general Maxwell equations.
The general equation is described in calculus:
dB = u/(2*pi) * [(J dV) x r]/r_mag^3
dB = differential magnetic field, a vector, measured in (Teslas / meter)
u = permeability of the medium the wire is in. In free space u = uo (4*pi*10^-7 Tesla * meters / Ampere)
J dV = current density vector in a differential volume
'x' = cross product
r = vector to where you want to calculate the magnetic field
r_mag = magnitude of that vector (aka distance)
If you are not familiar with calculus this equation may look rather difficult, but there are a couple of idealizations that simplify this calculation.
1) If our current is only 1 dimensional, the J becomes I (current).
2) By making the wire symmetric (either circular, straight, infinite, etc) we can get a much much much simpler closed form expression.
For an infinitely long, straight piece of wire: B = u*I/(2*p*r) Teslas, r is the distance radially away from the wire.
For a circular loop of wire: B = u*I/(2*R) Teslas, R is the radius of the circular loop.
So enough of the mathmatics, lets talk about what the equations mean. The math says that magnetic fields arise from moving charges (current) and that the magnetic fields are circles around the wire. It also says that it points in a direction (which makes sense since magnetic fields are vector fields). That direction is given by the cross product of the direction the current is going, with the direction away from the wire. The result is a vector that rotates either clockwise or counterclockwise around the wire.
I don't know if your familiar with the cross product, but the common way to picture what happens is to use three fingers, your middle finger, index finger, and your thumb. First make a fist, then point your thumb up, like a thumbs up. Then point your index away, like a pistol, and then make a right angle between your index and middle finger. All three fingers should be right angles with each other. This completely describes the cross product.
The index is the first vector (in this case the current), the middle finger is the second vector (the direction of where you want to calculate the magnetic field), and your thumb is the result (the magnetic field). So a quick example is picture a wire flowing through your monitor. Point your index finger in this direction. Now you want to calculate the direction of the magnetic field at the top left corner of your screen. So make your middle finger point to the top left corner. The direction your thumb is point in is the direction of the magnetic field (it should be pointing at the top right corner).
So I hope explained this well enough so you can calculate the field in some situations and can picture what the field looks like, all described by the Biot-Savart Law.
Selena Halvorson
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Can you prove Biot-Savart's law directly?
No, it was found by expirement.
Where will you use ampere circuital law in preference to biot savart law?
Depends on whether a path integral or a normal integral is easier to determine.
What is the difference between coulomb's law and biot savart law?
According to Coulomb's law, the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of distance between their centers. And Biot Savart's law gives the magnetic field at point due to a small current element. And, according to Biot Savart's law ,the magnitude of magnetic field is directly proportional to the product of current element Idl and Sin theta and inversely proportional to the square of distance between two point charges.
Derivation of amperes law from biot savart law?
----> ampere's law :which is to be used while finding magnetic fields inside the enclosed surface. we are allowed to use it to any surface however the surface have to be in such ways that the path must pass through the point and the path must have enough symmetry so that is constant along the large path of it!----> Biot Savart law : we often use biot savart to find magnetic fieldsgenerated by an electric current carrying wire of radius "r" and since the radius is perpendicular with I we don't worry about messy integration!thus we left with : dB =( µ_0 Idl) / (4πr^2)also knowing that l = 2πr helps so we substitute it in! and we eventually end up with : dB =( µ_0 Id2πr) /(4πr^2)Thus B = µ_0 I / 2πrCombining Ampere Law to Biot savart.Thus we can derive Biot savart from ampere by the following:§ B.dl = µ_0 I (encl)B § dl = µ_0 I (encl) hence B (2πr) isB(2πr) = µ_0 Iso B = (µ_0 I) / 2πrfaith nshuti.
Prove that current can be a source of magnetism?
A classic and ancient experiment is to get a compass, a battery (9volt is fine), and some wire. Notice that the compass changes when the circuit is closed (wire connected to the two terminals). You can also see that the compass gets affected less when it is far from the wire versus next to it. If your interested in the math behind the experiment, you may want to do some research on the Biot-Savart Law. The Biot-Savart law describe the magnetis field when the current is constant, or not time-varying. A more general form of the equation is called Ampere's Law, and the more general case of that is Maxwell's equations.
What is the differential form of Biot and Savart law?
Hi this is it : dB=m0I/4pi (dl x r) / |r3|, I hope this works for you.you can take r unitary if you change |r3| by |r2| and make cross product alotmuch simpleThis is took of my class of Electrodynamics 2
Magnetic field due to a current through a circular loop?
The magnetic field due to a constant current through a circular loop is the same shape, outside the loop, as the field due to a bar magnet. At the centre of the loop the field can be found, using the Biot-Savart Law, to be (Equation 1: URL in related links), where ?0 is the permeability of free space, I is the current through the loop, R is the radius of the loop and z-hat is a unit vector perpendicular to the plane of the loop. The field on the axis of the loop can be found, again using the Biot-Savart Law, to be (Equation 2: URL in related links), where z is the distance from the centre of the loop along its axis and all other symbols have the same meaning as in the previous equation.
When did Félix Savart die?
Félix Savart died in 1841.
When was Félix Savart born?
Félix Savart was born in 1791.
What is a biot?
A biot is another term for an abampere.
What is Le Biot's population?
Le Biot's population is 424.
When was Camille Biot born?
Camille Biot was born in 1850.
