The horizontal section of the conductor, the electrical resistance of which is 2.6 ohms, is located in a horizontal

The horizontal section of the conductor, the electrical resistance of which is 2.6 ohms, is located in a horizontal uniform magnetic field with an induction of 0.02 T perpendicular to the lines of magnetic induction. A voltage of 10.4 V is applied to the ends of the conductor. What is the length of the conductor if a force of 20 mN acts on the conductor from the side of the magnetic field?

The horizontal section of the conductor, the electrical resistance of which is R = 2.6 Ohm, is located in a horizontal uniform magnetic field with induction B = 0.02 T perpendicular to the lines of magnetic induction, that is, α = 90 °. A voltage U = 10.4 V is applied to the ends of the conductor, then, according to Ohm’s law, I = U / R. From the side of the magnetic field, a force F = 20 mN = 0.02 N. acts on the conductor.

To determine the length of the conductor L, we will use the law characterizing the Ampere force – the force of the interaction of the magnetic field and the conductor with the current: F = B ∙ I ∙ L ∙ sin α. Then:

L = F: (B ∙ U ∙ sin α) / R; L = F ∙ R: (B ∙ U ∙ sin α), we get,

L = 0.02 N ∙ 2.6 Ohm: (0.02 T ∙ 10.4 V ∙ sin 90 °); L = 0.25 m.

Answer: the length of the conductor was 0.25 m.