THE BIOT-SAVART LAW
(a) This law is applicable to a small current carrying conductor.
(b) It is an experimental law which gives the quantitative value of the magnetic field produced by a current element at any point in the space around it.
(c) Let `XY` be a conductor of an arbitrary shape carrying current `'i'` and `P` is a point in vacuum at which the field is to be determined. We consider an infinitesimal current element `AB` of length `dl` Its direction is that of the tangent to the conductor. Let r be the position vector of P making an angle `theta` with dl
( d) According to Biot-Savart's Law, the magnitude of magnetic field `dB` (also called magnetic flux density) at a point P due to current element dl or the current carrying conductor is
(i) Directly proportional to current, i.e., `dBpropi`
(ii) Directly proportional to elemental length, i.e., `dB prop dl`
( iii) Directly proportional to the sine of angle `theta` between `dvecl` & `vecr` i.e. `dBpropsintheta`
(iv) Inversely proportional to the square or distance `dBprop(1/r^2)`
Hence,
`dBprop (idlsintheta)/r^2` or `dB = mu_0/(4pi)\ \ (idlsintheta)/r^2` where `mu_0/(4pi) = 10^-7 Wb//A-m`
`mu_0` is called permeability of free space and its value is `4pi xx 10^-7N//A^2`
(e) `text(Direction of)` `dvecB`. The direction of magnetic field is along the direction of cross product `dvecl xx vecr` i.e. vector `dvecB` is perpendicular to both the current element `idvecl` and position vector `vecr`. The direction of `dvecB` a is represented by the
`text(Right Hand Rule :)`
If the thumb represents the current and we curl our fingers to pass through the point P, then the direction of the fingers at P gives the direction of magnetic field there. Remember, this law is applicable for straight current carrying conductor. Combining all the above factors, we can write
`dvecB = mu_0/(4pi) (i(dl xx vecr))/r^3` .........................................(1)
(f) `text(Superposition principle :)` Net magnetic field at a field point is equal to the vector sum of the individual magnetic fields at that point, i.e., `vecB_(n et) = vecB_1 + vecB_2.........................`
In accordance with the principle of superposition the total B is found as a result of integration of the equation (1) over all current elements.
(b) It is an experimental law which gives the quantitative value of the magnetic field produced by a current element at any point in the space around it.
(c) Let `XY` be a conductor of an arbitrary shape carrying current `'i'` and `P` is a point in vacuum at which the field is to be determined. We consider an infinitesimal current element `AB` of length `dl` Its direction is that of the tangent to the conductor. Let r be the position vector of P making an angle `theta` with dl
( d) According to Biot-Savart's Law, the magnitude of magnetic field `dB` (also called magnetic flux density) at a point P due to current element dl or the current carrying conductor is
(i) Directly proportional to current, i.e., `dBpropi`
(ii) Directly proportional to elemental length, i.e., `dB prop dl`
( iii) Directly proportional to the sine of angle `theta` between `dvecl` & `vecr` i.e. `dBpropsintheta`
(iv) Inversely proportional to the square or distance `dBprop(1/r^2)`
Hence,
`dBprop (idlsintheta)/r^2` or `dB = mu_0/(4pi)\ \ (idlsintheta)/r^2` where `mu_0/(4pi) = 10^-7 Wb//A-m`
`mu_0` is called permeability of free space and its value is `4pi xx 10^-7N//A^2`
(e) `text(Direction of)` `dvecB`. The direction of magnetic field is along the direction of cross product `dvecl xx vecr` i.e. vector `dvecB` is perpendicular to both the current element `idvecl` and position vector `vecr`. The direction of `dvecB` a is represented by the
`text(Right Hand Rule :)`
If the thumb represents the current and we curl our fingers to pass through the point P, then the direction of the fingers at P gives the direction of magnetic field there. Remember, this law is applicable for straight current carrying conductor. Combining all the above factors, we can write
`dvecB = mu_0/(4pi) (i(dl xx vecr))/r^3` .........................................(1)
(f) `text(Superposition principle :)` Net magnetic field at a field point is equal to the vector sum of the individual magnetic fields at that point, i.e., `vecB_(n et) = vecB_1 + vecB_2.........................`
In accordance with the principle of superposition the total B is found as a result of integration of the equation (1) over all current elements.