Find the magnitude and direction of the magnetic field at the point equidistant

Question

Find the magnitude and direction of the magnetic field at the point equidistant from the wires in Figure 21.57(a), where x = 20.0cm and I1 = 5.00 A. Use the rules of vector addition to sum the contributions from each wire. Magnitude

Explanation / Answer

the point equidistant from all the 3 wires will be at the centre of the equilateral triangle formed by the three wire. distance of the middle point can be given by, d = (x/2)/cos30 => 0.58 *x = 0.58*20 = 11.6 cm magnetic field due to a current carrying infinite wire = (u0*I)/(2*pi*d) = (2*10^-7*I)/d magnetic field due to wire carrying I=5A is = (2*10^-7*5)/0.116 = 8.62*10^-6 T (counterclockwise from the x-axis) => B1 = +8.62*10^-6 T magnetic field due to wire carrying I=20A is = (2*10^-7*20)/0.116 = -3.45*10^-5 T => B2 = -3.45*10^-5 T similarly B3 = (2*10^-7*10)/0.116 = -1.72*10^-5 T so, net B = B1 + B2 +B3 = (8.62 -34.5 - 17.2)*10^-6 = -4.31*10^-5 T counterclockwise from x-axis

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