Q. A current of is flowing on the sides of an equilateral triangle of side . The magnetic field at the centre of the triangle will be :

 3901  228 JEE MainJEE Main 2018Moving Charges and Magnetism Report Error

Solution:

The triangle shown here can be considered to be having three finite wires of length a each. We need to find the magnetic field at a point on the perpendicular bisector of this wire.
The magnetic field due to a finite wire at a distance from the wire, making angles and w.r.t the ends of the wire is given by

This point is the same for all the three wires and at a distance of from the wire. The direction of the magnetic field at that point is inwards due to all the wires. Thus, if is the magnetic field due to one wire, then total magnetic field due to three wires will be acting inwards

The distance can be expressed in terms of a by the formula . Substituting for in the previous expression, we get,