# Direction and the current in wire segment de flows in

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direction and the current in wire segmentDEflows in the-ˆkdirection.xzAGaaTop ViewBBBˆı-ˆkˆı-ˆkBBBThe magnetic force on a wire is given byFmag=I×B .The vectoris given by the sum of thecurrent segments=-→AC+-→CD+-→DE+-→EG,and this is the vector-→AG,(see figure above).The magnitude is given byF×Bı-ˆk)×ı)= (ˆı×ˆı)-(ˆk×ˆı)= 0-ˆF=-ˆ.009
10.0 pointsAdevice(“source”)emitsabunchofcharged ions (particles) with a range of ve-locities (see figure).(the charge on each ionis q.)Some of these ions pass through theleft slit and enter “Region I” in which thereis a vertical uniform electric fieldE(in the-ˆdirection) and a uniform magnetic fieldB(aligned with the±ˆk-direction) as shown inthe figure by the shaded area.qmRegion ofMagneticFieldB+VdxyzrRegion IRegion II
Munoz (gm7794) – HW06 – TSOI – (92515)
5Figure:ˆıis in the direction +x(to the right), ˆis in the direction+y(up the page), andˆkis in thedirection +z(out of the page).The ions that make it into “Region II” areobserved to be deflected downward and thenfollow a circular path with a radius ofr.What is the mass of the ions?=q B2rE01010.0 pointsWhat current is required in the windings ofa long solenoid that has 434 turns uniformlydistributed over a length of 0.419 m in orderto produce inside the solenoid a magnetic fieldof magnitude 0.0001096 T? The permeablityof free space is 1.25664×10-6T m/A.
6The magnetic field of the wire isB=μ0I2πr=(1.25664×10-6T·m/A) (0.549 A)2π(0.927 m)=1.18447×10-7T.01210.0 pointsA proton and an electron enter the same mag-netic field with identical velocities at rightangles to the field.What would be the ratio of the radius ofthe circular orbit of the proton to the radiusof the electron’s orbit?1.1 : 12.4×106: 13.1 : 4×1064.1 : 20005.2000 : 1correctExplanation:Let :mp2000me,vp=ve,andqp=qe.When an atomic particle of chargeqis shotinto a magnetic field with a velocityvat rightangles to the direction of the fieldB, theradius of the circular orbit can be expressedbyr=m vB qm .Thus, the ratio of the radii isrpre=mpme=2000.01310.0 pointsA duck flying due north at 84 m/s passes over
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