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plese solve them and post the solution thoroughly.

Asked by Arushi Juyal 12th December 2017, 7:15 AM
Answered by Expert
Answer:
Two charged particles having charge of same magnitude, but opposite sign and same mass.
 
Since they are prjected in opposite direction the direction of deflection is same. Hence they will travel in a circular motion as shown in figure (v1 > v2).
 
angular momentum of charged particle moving in magnetic field is given by L = m × v × r , where r is radius of curvature
 
radius of curvature can be obtained from q×B×v = m(v2/r).
 
Hence L = m × v × [ mv/ (qB) ] = m2v2 / (qB)
 
velocity of Particle-B with respect to particle-A is v2-v1.
 
Hence angular momentum of particle-B with respect to particle-A is
 begin mathsize 12px style L space equals space fraction numerator m squared over denominator q B end fraction open parentheses v subscript 2 minus v subscript 1 close parentheses squared space equals space fraction numerator m squared over denominator q B end fraction open parentheses v subscript 2 superscript 2 space plus space v subscript 1 superscript 2 space minus space 2 v subscript 1 v subscript 2 close parentheses
sin c e space open vertical bar v subscript 1 close vertical bar space almost equal to space open vertical bar v subscript 2 close vertical bar space space b u t space v subscript 1 space greater than space v subscript 2 space comma space w e space c a n space w r i t e space L space equals space fraction numerator m squared over denominator q B end fraction open parentheses v subscript 2 superscript 2 space plus space v subscript 1 superscript 2 space minus space 2 v subscript 2 superscript 2 close parentheses space equals space space fraction numerator m squared over denominator q B end fraction open parentheses v subscript 1 superscript 2 space minus space v subscript 2 superscript 2 close parentheses end style

angular momentum of particle-B with respect to particle-A is proportional to begin mathsize 12px style space open parentheses v subscript 1 superscript 2 space minus v subscript 2 superscript 2 close parentheses end style
Answered by Expert 15th December 2017, 1:18 PM
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