A positively charged particle is given an initial velocity v_(0) in XY plane as shown in diagram. Initially the particle was at origin and the region contains uniform, mutually perpendicular electric and magnetic field. Let vecE=-Ehatj and vecB=Bhatk. The minimum magnitude of the magnetic field so that the charge particle crosses the origin again during its subsequenty motion is B_("min")=(npiE)/(v_(0)), find the integer value n

A positively charged particle is given an initial velocity v_(0) in XY

1.	A positively charged particle is given an initial velocity v_(0) in XY plane as shown in diagram. Initially the particle was at origin and the region contains uniform, mutually perpendicular electric and magnetic field. Let vecE=-Ehatj and vecB=Bhatk. The minimum magnitude of the magnetic field so that the charge particle crosses the origin again during its subsequenty motion is B_("min")=(npiE)/(v_(0)), find the integer value n
Answer» Solution :`vecv=(v_(0))/2 (SQRT(3HATI)+HATJ)` For corssing ORIGN, `k(2pim)/(QB)=(2(v_(0)//2))/(qE//m),k` is an integer `impliesB=((2piE)/(v_(0)))k` For minimum value, `k=1` `impliesB_("min")=(2piE)/(v_(0))`

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