Answer to Question #235385 in Electricity and Magnetism for Angel

Question

Question 2 [6 marks]

Two straight, parallel conductors situated a distance l (ℓ )from each other carry currents in opposite directions as shown below. One conductor carries a current of 1.0 A and the other carries a current of 3.0 A. The magnitude of the magnetic flux density at a point that is distance l (ℓ ) to the right of the right conductor is BR and that at another point that is distance l (ℓ ) to the left of the left conductor is BL. Determine the ratio BL/BR. Note that only the points at which BR and BL are measured and not their directions are shown on the diagram. You will therefore need to take the directions of the constituent flux densities into account at each point.

S2 TT5 Fig 1 -21.png

Answer 1

$B_i=B_j+B_k=\frac{\mu\mu_0}{2\pi}(\frac{I_j}{l_j}+\frac{I_k}{l_k}),$

$\frac{B_L}{B_R}=\frac{\frac{I_1}{l}+\frac{I_2}{2l}}{\frac{I_2}{l}+\frac{I_1}{2l}}=\frac{2I_1+I_2}{2I_2+I_1}=\frac 57.$