A wire is bent so that it forms the arc of two partial circles complete except f

Question

A wire is bent so that it forms the arc of two partial circles complete except for an angle a, and these partial circles are connected by two radial pieces as shown. The inner partial circle has a radius R1, and the outer partial circle has a radius R2. The center of the circles is the point C. A current I goes through the wire as shown.

a.     a. use the Boit-Savart law to find the magnetic field at the point C due to current in both straight radial wires Bstraight

b.     b. Use the Boit-Savart law to find the magnetic field at the point C due to current in the outer inner partial circle of wire Binner.

c.      c. Use the Boit- Savart law to find the magnetic field at the point C due to current in the outer partial circle of wire Bouter.

d.     d. Find the net magnetic field at the point C, Bnet.

Explanation / Answer

a) B1 = B2 = (mue/4*pi) *I*dL*sin(0)/r^2 = 0

b) B2 = [(2*pi-alfa)/2*pi]*mue*I/(2*R1)( in to the paper plane)

c) B3 = [(2*pi-alfa)/2*pi]*mue*I/(2*R2)(out of the paer plane)

d) Bnet = B2-B3 = [(2*pi-alfa)/2*pi]*mue*I/2 *(1/R1-1/R2)

here Bnet is into the paper plane

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