part b explanation optional just want to see an approach for a In this problem we will compare the magnitudes of electri

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part b explanation optional just want to see an approach fora
In this problem we will compare the magnitudes ofelectrical force qE and magnetic force qv × B on a moving testcharge q due to fields E and B produced by another charge Q at somedistance r.
a) Let E be the static Coulomb field of Q with magnitude Q .Also let B the magnetic field 4πǫor2 calculated using Biot-Savartlaw with a maximum magnitude μoI|dl| where for I|dl| we can use4πr2 QVs, where Vs denotes the speed of charge Q when it is movingto produce B. Denoting the speed of the test charge as vq, showthat the magnetic force on q can be as strong as the electric forceonly in the limit when the product of vq and Vs approaches c2 ≡ 1 ,where c ≈ 3 × 108 μoǫo m/s. Hint: what is the expression for thelargest possible ratio of the magnitudes of qvq × B and qE?
b) The result of part (a) shows that magnetic force is typicallymuch weaker than the electro- static force (when elementary sourcesare considered one at a time). Why then are magnetic effectsobserved in everyday life (e.g., pull and push of refrigeratormagnets) often stronger than electrostatic effects (e.g., staticthat you experience while taking off your sweater)? Discuss.