What is the direction and magnitude of the magnetic field at the center of the c

Question

What is the direction and magnitude of the magnetic field at the center of the circular wire due to two contributions: from the circular wire and the straight wire. The current is I = 10 A. The straight wire is infinitely long. The radius of the circular wire is R = 0.5 m. The gap width is W. Find the solution for B neglecting W so that ( R >> W). Find correction in your solution for B if W is not small. (is not it tricky?) Will your solution change for (a) if we re-direct the current direction in the circular section, but keep current the same in the straight wire?

Explanation / Answer

a)Magnetic Field due to wire = u*I/2*pi*r and the direction will be out of the wire. I=10A, r=0.5m B= 40T Circular part will have the same magnetic field but in the opposite direction i.e inside the plane of paper. SO, net magnetic firld at the centre will be zero c) ie the direction of current is reversed in the circular section, then the two sections will have the megnetic field in the same direction and hence net magnetic field at the centre will be 2*40=80T

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