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hw10 - Physics 21 Fall 2008 Solution to HW-10 27-1 A...

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Physics 21 Fall, 2008 Solution to HW-10 27-1 A particle with a charge of q = 1 . 10 × 10 8 C is moving with instantaneous velocity v = (5 . 00 ˆ i 3 . 70 ˆ j ) m/s. (a,b,c) Find the x , y , and z components of the force exerted on this particle by a magnetic field B = 1 . 50 ˆ i T. (d,e,f) Find the x , y , and z components of the force exerted on this particle by a magnetic field B = 1 . 50 ˆ k T. (a,b,c) F = q v × B = q ( v x ˆ i + v y ˆ j ) × B ˆ i Using ˆ i × ˆ i = 0 and ˆ j × ˆ i = ˆ k leads to F = qv y B ˆ k = 6 . 11 × 10 8 N ˆ k (d,e,f) F = q v × B = q ( v x ˆ i + v y ˆ j ) × B ˆ k Using ˆ i × ˆ k = ˆ j and ˆ j × ˆ k = ˆ i leads to F = qB ( v y ˆ i v x ˆ j ) = (6 . 11 × 10 8 ˆ i + 8 . 25 × 10 8 ˆ j ) N 27-8 A particle with charge 6 . 00 nC is moving in a uni- form magnetic field B = 1 . 30 ˆ k T. The magnetic force on the particle is measured to be F = 3 . 70 × 10 7 ˆ i + 7 . 60 × 10 7 ˆ j N. (a) Are there components of the velocity that are not determined by the measurement of the force? (b,c) Cal- culate the x and y components of the velocity of the particle.
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