Figure (a) shows two wires, each carrying a current. Wire 1 consists of a circul

Question

Figure (a) shows two wires, each carrying a current. Wire 1 consists of a circular arc of radius R = 0.021 m and two radial lengths; i_1 carries current ii = 1.8 A in the direction indicated. Wire 2 is long and straight; it carries a current i_2 that can be varied; and it is at distance R/2 from the center of the arc. The net magnetic field B due to the two currents is measured at the center of curvature of the arc. Figure (b) is a plot of the component of B in the direction perpendicular to the figure as a function of current i_2. The horizontal scale is set by i_2S = 2.0 A. What is the angle (in rad) subtended by the arc?

Explanation / Answer

magnetic field dueto both conductors

= in radians .For B=0 so i2 = 1A = 4 ( i2 / i1)

B =0

x=phi

uoI1*x/4piR -uoI2/2pi(R/2)=0

I1*x=4I2

X=4(i2/i1) =4*(1/1.8)

x=2.22 rad

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