A circular wire loop of mass M and radius R carries a current I . It hangs from a hinge that allows it to swing in the direction perpendicular to the plane of the loop. A uniform magnetic field B exists everywhere in space pointing upwards. What angle THETA does the plane of the loop make with the vertical when it is in static equilibrium?
THETA =90
@anton, have you check the answer?
To find the angle θ, we can use the equilibrium condition for a wire loop in a magnetic field. In static equilibrium, the gravitational force pulling the loop downward is balanced by the magnetic force acting on the current-carrying loop.
The gravitational force pulling the loop downward can be calculated using the equation F_gravity = mg, where m is the mass of the wire loop.
The magnetic force acting on the current-carrying loop can be calculated using the equation F_magnetic = I * L * B * sin(θ), where I is the current in the wire loop, L is the circumference of the loop (L = 2πR), B is the magnetic field strength, and θ is the angle between the plane of the loop and the vertical axis.
In static equilibrium, the gravitational force is equal to the magnetic force, so we have:
mg = I * L * B * sin(θ)
To find the value of θ, we can rearrange the equation as follows:
θ = arcsin((mg) / (I * L * B))
Substituting L = 2πR:
θ = arcsin((mg) / (2πIRB))
Therefore, the angle θ that the plane of the loop makes with the vertical in static equilibrium can be found using the equation θ = arcsin((mg) / (2πIRB)).