A strong magnet is placed under a circular ring with a radius of R flowing current i as shown below. Obtain the magnitude and orientation of the magnetic force acting on the ring when the magnetic field strength vector at the ring position forms an angle of θ from the vertical position.

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A strong magnet is placed under a circular ring with a radius of R flowing current i as shown below. Obtain the magnitude and orientation of the magnetic force acting on the ring when the magnetic field strength vector at the ring position forms an angle of θ from the vertical position.

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Step 1

Given that, Shape of the Conductor is a circular coil

Magnetic field B at the ring position forms an angle of θ from the vertical position.

Angle that gives magnetic force is θ

Circumference/ Length of the coil,l=2πr

 

Step 2

The magnetic force on each part of the ring is Idl × B=IdlB

Advanced Physics homework question answer, step 2, image 1Advanced Physics homework question answer, step 2, image 2

Taking y component from sketch diagram,

F=i dl B sinθ jFy=dF=02π irdφBsinθ=irBsinθ02πdϕFy=2πriBsinθ

Whereas Fx will be zero because in symmetric ring i^ components will be canceled out by the opposite portion.

In that case, Fx=0 for symmetric ring

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