A small bar magnet experiences a torque when the axis of the magnet is at to a magnetic field. What is the magnitude of its magnetic dipole moment?
The magnitude of its magnetic dipole moment is .
We need to find the magnitude of its magnetic dipole moment.
The torque represents the magnitude of the force multiplied by the distance between the axis and the line of the action. A current loop inside a magnetic fields experiences a torque that is exerted by the magnetic force and the loop starts to rotate. For a square loop with side , its torque is given as:
where represents the magnetic dipole moment of the loop, is the current in the loop and is the angle between the magnetic field and the magnetic dipole moment of the loop.
When the dipole moment is parallel to the magnetic field, the torque is zero and it is maximum when the dipole moment is perpendicular to the magnetic field. Our target is to find Therefore we rearrange equation (1) for to be in the form of :
Now, We plug the values for into equation (2) to get :
Your employer asks you to build a -cm-long solenoid with an interior field of . The specifications call for a single layer of wire, wound with the coils as close together as possible. You have two spools of wire available. Wire with a gauge has a diameter of and has a maximum current rating of . Wire with a gauge is in diameter and can carry up to . Which wire should you use, and what current will you need?
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