CBSE Class 12-science Answered
Six parallel aluminum wires of small, but finite, radius lie in the same plane. The wires are separated by equal distances d, and they carry equal currents I in the same direction. Find the magnetic field at the center of the first wire. Assume that the current in each wire is uniformly distributed over its cross section.
A schematic layout of the problem is shown in the following figure:
The magnetic field generated by a single wire is,
where r is the distance from the center of the wire.
This equation is correct for all points outside the wire, and can therefore be used to determine the magnetic field generated by wire 2, 3, 4, 5, and 6. The field at the center of wire 1, due to the current flowing in wire 1, can be determined using Ampere's law, and is equal to zero. The total magnetic field at the center of wire 1 can be found by vector addition of the contributions of each of the six wires. Since the direction of each of these contributions is the same, the total magnetic field at the center of wire 1 is equal to
B = B2+ B3 + B4 + B5 + B6