Question

A particle with a charge of − 5.20 nC is moving in a uniform magnetic field of B⃗ =−( 1.21 T )k^. The magnetic force on the particle is measured to be F⃗ =−( 3.70×10−7 N )i^+( 7.60×10−7 N )j^. Calculate the scalar product v⃗ ⋅F⃗ . Work the problem out symbolically first, then plug in numbers after you've simplified the symbolic expression.

Answer 1

force in magnetic field F = q(VxB) , let V = Xi +Y j + Z k

=> −( 3.70×10^-7)i + ( 7.60×10^-7 )j = q*[(X i + Y j + Z k) x (-1.21 k) ]

=> −( 3.70×10^-7)i + ( 7.60×10^-7 )j = q*[ 1.21X j - 1.21 Y i ] = (-5.20*10^-9)*1.21*( -Y i + X j)

=> −( 3.70×10^-7)i + ( 7.60×10^-7 )j = - 6.292*10^-9*( -Yi + Xj )

=> X = - 1.207*10^2 m/s , Y = - 0.588*10^2 m/s

=> V = (-120.7 i - 58.8 j) m/s  

magnitude of V = [ (-120.7)^2 + (-58.8)^2 ]^0.5 = 134.26 m/s

magnitude of F = [(-3.7*10^-7)^2 + (7.60*10^-7)^2]^0.5 = 8.45*10^-7 N

=> V.F = 134.26*8.45*10^-7 = 1.134*10^-4 Nm/s