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Question:

A conductor lies along the z-axis at 0.5m ≤ z < 1.5m and carries a fixed current of 10.0A in -az direction (see figure). For a field B = 3.0 × 10⁻⁴(0.2x) ay T, the power required to move the conductor at constant speed to x = 2.0m and y = 0m in 5 × 10⁻⁷s is (Assume parallel motion along the x-axis)

14.85W

29.7W

2.97W

1.57W

Solution:

P=Work Done/Time = ∫F.dx/t = ∫IlB.dx/t = ∫(10)(10)(3×10⁻⁴)(0.2x)dx/(5×10⁻⁷) = 9 × 10⁷ × 10⁻⁷[e⁰⋅²ˣ]⁰² = 9[1 - e⁻⁰⋅⁴] = 2.97W