Physics - Magnetism Question with Solution | TestHub
To break an electrical circuit when the current increases, a movable thin semicircular ring OA (figure) is used. The ring has a mass and a radius , and it can freely (without friction) rotate in the vertical plane about point O . The system is located in a uniform horizontal magnetic field with an induction , perpendicular to the plane of the figure. Find the maximum current strength (in A) at which the limiter disconnects the circuit.
Answer:
Solution:
Put the centre of the circular arc at , with pivot . For an arc element at angle :
The field is perpendicular to the plane. Integrating the moment of the magnetic force about O gives
The semicircular wire has its centre of mass directly above the circle centre, so its horizontal lever arm from O is R:
At the threshold, the magnetic and gravitational moments balance:
