A 80 mu C magnitude charge is travelling with a speed of 40

A 8.0 mu C (magnitude) charge is travelling with a speed of 4.0 -10^5 m/s when it enters a magnetic field of strength 1.5 T. For each situation below do the following use traditional Cartesian coordinate system where the X-Y plane is the plane of the paper and \"+i\" is the right and \"+j\" is up Express V, B in i, j, k format Determine the magnetic force on the charge expressed in i, j, k format Draw a picture showing the direction of V, B and F. Can use 2 d picture and \"O\" and \"X\" Use \"O\" and \"X\" as symbols for out of and into the plane of the paper respectively

Solution

F = q v x B

v x B = [3.7 x 10⁵j] x [1.4 i + 2.1 j]

v x B = [(3.7 x 10⁵)(1.4) (j x i)] + [(3.7 x 10⁵)(2.1)(j x j)]

j x i = - k

j x j = 0

v x B = (3.7 x 10⁵)(1.4) ( - k)

F = q v x B = ( - 1.6 x 10 ^{- 19}) (3.7 x 10⁵)(1.4) ( - k)

F = ( 1.6 x 10 ^{- 19}) (3.7 x 10⁵)(1.4) (k)

F = 8.29 x 10 ^{- 14} N k