2. A set of four wires with circular cross-section and radius rocarry time-independent currents as illustrated in Figure 1. The wires are in air. The current density in wire 1 is \vec{J}_{1}(r)=\alpha_{0} \sqrt{r} \hat{k} where of r is the distance from the centre of wire 1. The numerical labels enumerate the wires, and L is the distance between the centres of neighbouring wires. a. Determine an expression for the magnetising field strength, H(r), in terms of r, ao, ro and any relevant physical constants. Consider only wire 1 in your analysis. b. If wires 2, 3 and 4 carry twice the magnitude of current density of wire 1, determine an expression for the total magnetic flux density along the z-axis through the origin(Figure 1). Take the wires to be equidistant from this line.Represent your answer in the Cartesian co-ordinate system shown on Figure 1 in terms of ao, ro, L and any relevant physical constants. c. At a time t = 0 s an electron located at the origin is moving with a velocity i = vok. Determine an expression for the force it experiences at time t = 0 s in terms of ao,ro, vo, L and any relevant physical constants. d. If the four constants are a, = 5 x 10° A/m³/2, ro = 1 mm,L = 1 cm and vo = 8.4 x 102 m/s, determine the magnitude and direction of the force the electron experiences at t = 0 s. e. Comment briefly upon the subsequent trajectory of the electron.

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