Answer to Question #258522 in Electricity and Magnetism for Ali

Question

Consider the following situation shown below. A mass, m = 1.8 kg, is hung from a conducting wire shaped into a loop. The dimensions of the loop are 2m x 1.8m. Part of the loop is in a region where a uniform magnetic field (B = 1.6T) is into the page everywhere. (Each part 10 pts; 20 pts total)

https://ibb.co/1nG4v5v

If there were a current in the wire loop,

a) which direction would the current have to flow in order for the wire to be at rest and not fall? Show your work and explain your reasoning.

b) what would the magnitude of the current have to be in order for the wire to be at rest and not fall? Show your work and explain your reasoning. Use an additional sheet if necessary.

Answer 1

a) The current should flow in clockwise direction because this way it would create a force that points upward: the field lines go into the screen, the current in the upper wire is to the right, therefore, the force is upward by the left-hand rule. The force will oppose the force of gravity.

b) The magnitude of the force can be found from the following equation:

$$F=BIL=mg,\\\space\\ I=mg/(BL)=5.5\text{ A}.$$