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# hw10 - Physics 21 Fall 2009 Solution to HW-10 27-1 A...

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Physics 21 Fall, 2009 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 27.6 An electron moves at v = 2 . 20 × 10 6 m/s through a region in which there is a magnetic field of unspecified direction and magnitude B = 8 . 00 × 10 2 T. (a) What is the largest possible magnitude of the acceleration a of the electron due to the magnetic field? (b) What is the smallest possible magnitude of the acceleration of the electron due to the magnetic field?

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