Did you know that the Biot-savart law governs the electromagnetic field of a wire loop, and is commonly used to calculate the magnetic fields produced by such loops in biots law? You can master the art of Biot-savart law with these 8 tips!
Here are the 8 tips:
1. A current I (in Ampères) flowing through a circular coil at radius r (in meters) will produce a magnetic flux Φ( in Tesla, T). The flux density is given by Φ = μ o I/2πr. A Tesla is equivalent to 10,000 Gauss or 100 Maxwells.
2. The electric field H (in Volt/meter) produced at a distance d (in meters) from the coil is given by H = I2/4πd, where Φ = μ o I/2πr.
3. If you place a key under the coil, the line integral of E(qx, r) in the x direction has to be zero. The line integral of E'(qy, r) in y direction is zero as well. This is called Gauss’s Law of Magnetic Fields .
4. If you place an iron bar near the center of the wire loop, the area enclosed will be very small compared to the area enclosed if there was no magnet close by. This is called Lenz ‘s Law .
5. If you place a magnet at one end of the wire loop, its magnetic field will dominate that produced by the coil. This is called Faraday’s Law .
6. If a current I flows through a wire loop producing magnetic flux Φ and voltage V = IR then phasor P will be given by : the integral of E(qx, r) from 0 to r is equal to q2E(qx, r), where q = V/IR.
7. If you place an iron bar near one end of the wire loop, its area enclosed will be very small compared to the area enclosed if there was no magnet close by. This is called Lenz ‘s Law .
8. If you keep the current and voltage constant in a loop, then the amount of energy changing from one side to another side is equal to the work done by the magnetic field in producing this change. This is called Joule ‘s Law .
What about a path integral?
When you integrate paths over a wire loop which has current and magnetic flux, then it will include both the magnetic flux through Φ and also its time derivative. This gives a path integral of both electric field (H) to its time derivative and curl of magnetic field (H’= -Φ/d). You should be able to calculate both sides of this equation.
Common mistakes made are:
1. The magnetic field produced by the wire loop is not the same as the magnetic flux Φ.
2. If a rectangular loop has current and magnetic flux, then it can be shown to have vectors of electric field and curl of magnetic field.
3. The Biot-savart law does not govern the electromagnetic field of a wire loop alone, rather it governs in the interaction between a current flowing through a wire loop (including its time derivative) and an externally applied magnetic field (including its time derivative). This interaction is called Ampere’s Law .
a. If the current I is in Ampere, then the rate of change of electric field E (in Volt/meter) is given by : E = qe, where q = V/I and e = 1.60 af / (ε 0 t2) is called the permittivity of free space.
b. If the magnetic field H is in Gauss and ε0 = 8,000 C/molek, then the rate of change of magnetic flux Φ (in Tesla) will be given by : Φ = μ o I/2πr where H=H(t)=H/(t2).
c. If the magnetic field H is in Gauss and ε0 = 8,000 C/molek, then the rate of change of electric field E (in Volt/meter) will be given by : e = qe, where q = V/I and e = 3.2·10-18 × (ε 0 + ε 0 )t2 is called the permittivity of free space.
d. If a current I flows through a wire loop producing magnetic flux Φ and voltage V = IR then phasor P will be given by : -qE(qx, r) where r is the radius in meters of the wire loop.
4. Faraday’s Law states that magnetic moments are induced in proportion to the rate at which the impressed magnetic field varies in time, not the rate of change of the magnetic flux through a wire loop.
5. If you place an iron bar very close to one end of a wire loop, it will shield part of its magnetic flux, but if you place it anywhere else (away from one end), it will have no effect on the amount of flux passing through.
6. If you place an iron bar at the midpoint of the wire loop, then its area enclosed will be very small compared to the area enclosed if there was no magnet close by. This is called Lenz ‘s Law .
7. If you keep the current and voltage constant in a loop, then the amount of energy changing from one side to another side is equal to the work done by the magnetic field in producing this change. This is called Joule ‘s Law .
8. A current I (in Ampere) flowing through a circular coil at radius r (in meters) will produce a magnetic flux Φ( in Tesla, T). The flux density is given by Φ = μ o I/2πr. A Tesla is equivalent to 10,000 Gauss or 100 Maxwells.
