Four identical straight conductors are placed separately in the same uniform magnetic…

MATHEMATICS · Multi-part · ISC · Mathematics · Physics · Magnetic Effects of Current and Magnetism

Problem

Four identical straight conductors are placed separately in the same uniform magnetic field. Their individual parameters are given below. Arrange the conductors in descending order of the force they experience and justify your answer with calculations. (a) Conductor A: \; I=6 AI = 6\,\text{A}, L=0.20 mL = 0.20\,\text{m}, B=0.30 TB = 0.30\,\text{T}, θ=90∘\theta = 90^{\circ} (b) Conductor B: \; I=4 AI = 4\,\text{A}, L=0.25 mL = 0.25\,\text{m}, B=0.45 TB = 0.45\,\text{T}, θ=90∘\theta = 90^{\circ} (c) Conductor C: \; I=10 AI = 10\,\text{A}, L=0.15 mL = 0.15\,\text{m}, B=0.20 TB = 0.20\,\text{T}, θ=60∘\theta = 60^{\circ} (d) Conductor D: \; I=5 AI = 5\,\text{A}, L=0.30 mL = 0.30\,\text{m}, B=0.25 TB = 0.25\,\text{T}, θ=30∘\theta = 30^{\circ} (e) (i) Calculate the magnitude of the force on each conductor. (f) (ii) Rank the conductors from the one experiencing the greatest force to the one experiencing the least, showing your working clearly. (g) (iii) Find the ratio of the largest force obtained to the smallest force obtained.

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