9.1.5. A conductor of mass $0.16$ kg and length $80$ cm is suspended horizontally in a vertical uniform magnetic field on two thin threads. The ends of the conductor are connected to a current source by flexible wires located outside the field. Find the angle by which the suspension threads deviate from the vertical if a current of $2$ A flows through the conductor and the magnetic field induction is $1$ T.
Solution
Forces acting on the system
Ampere force acting on a conductor $$F = Il\cdot B$$ From Newton's second law, the condition of equilibrium on the horizontal and vertical axes $$T\cos\alpha = mg;\quad T\sin\alpha = F$$ dividing one expression by the other, we get $$\tan\alpha = \frac{F}{mg}$$$$\boxed{\alpha = \arctan \left(\frac{IlB}{mg}\right) = 45^{\circ}}$$
