Aparticleundergoesuniformcircularmotionofradius26.1µminauniformmagneticfield.Themagneticforceontheparticlehasamagnitudeof1.60×10-17N.Whatisthekineticenergyoftheparticle?

Short Answer

Expert verified

Thekineticenergyoftheparticleis2.09×10-22J.

Step by step solution

01

Listing the given quantities

Radiusr=26.1μm=26.1×10-6m.MagneticforceF=1.60×10-17N

02

Understanding the concept of kinetic energy and centripetal force

Weusetheformulaofcentripetalforcetoderivetheformulaofkineticenergy,andthen,usingthegivenvalues,wecanfindthekineticenergyoftheparticle.Formula:Centripetalforce,F=mv2rKineticenergy,K=12mv2

03

Explanation

Sincecentripetalforceisequaltomagneticforce,theexpressioncanbewrittenas:F=mv2rFr=mv2But,wehave,KE=mv22Therefore,KE=mv22=Fr2=1.60×10-1726.1×10-62=2.09×10-22J.Therefore,thekineticenergyoftheparticleis2.09×10-22.

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