NIELIT University(Govt. of India Institution) B.Tech/ M.Tech
ApplyLast Date to Apply : 15th September | Campuses in Agartala, Aizawl, Ajmer, Aurangabad, Calicut, Imphal, Itanagar, Kohima, Gorakhpur, Patna & Srinagar
Magnetic Field due to current in straight wire is considered one of the most asked concept.
56 Questions around this concept.
The magnetic field at the origin due to the current flowing in the wire as shown in figure below is
Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current and COD carries a current
. The magnetic field on a point lying at a distance d from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by
Magnetic Field due to current in a straight wire:
Magnetic field lines around a current-carrying straight wire are concentric circles whose centre lies on the wire.
The magnitude of magnetic field B, produced by a straight current-carrying wire at a given point is directly proportional to the current I pairing through the wire i.e. B is inversely proportional to the distance 'r' from the wire as shown in the figure given below.
Derivation:
The directions of magnetic fields due to all current elements are the same in the figure shown, we can integrate the expression of magnitude as given by Biot-Savart law for the small current element dy as shown in the figure
In order to evaluate this integral in terms of angle $\varphi$, we determine đy, x and \theta in terms of perpendicular distance "r" (which is a constant for a given point) and angle " ". Here,
Substituting in the integral, we have :
Taking out I and r out of the integral as they are constant :
Integrating between angle and
, we have
:
Note: is taken because it is measured in the opposite sense of
with respect to the reference line ( negative x-axis here)
Magnetic field due to a current-carrying wire at a point P which lies at a perpendicular distance r from the wire, as shown, is given as:
From figure,
Hence, it can be also written as
Different cases:
Case 1: When the linear conductor XY is of finite length and the point P lies on it's perpendicular bisector as shown
Case 2: When the linear conductor XY is of infinite length and the point P lies near the centre of the conductor
Case 3: When the linear conductor is of semi-infinite length and the point P lies near the end Y or X
Case 4: When point P lies on the axial position of the current-carrying conductor then magnetic field at P,
Note:
"Stay in the loop. Receive exam news, study resources, and expert advice!"