Consider a 3D coordinate system, (x, y, z) defined by the usual right-handed uni

Question

Consider a 3D coordinate system, (x, y, z) defined by the usual right-handed unit vectors: i times j = k, j times k = i, k times i = j A wire with a current I = 4.5 A is oriented such that the current travels in the -x direction. The wire is in a magnetic field given by: B = B_x i + B_z k where B_x = 3.3 times 10^-2 T and Bz = -3.8 times 10^-2 T. What is the y-component of the force on a 2.0 m length of this wire? Indicate the direction of the force with the correct sign for your answer. A positive answer means a force in the +y direction, and negative answer means a force in the -y direction. Give your answer in Newtons to at least 3 significant digits (3 digits to avoid round-off error)

Explanation / Answer

Current i = 4.5 A

Length L = (2m) (-i)

Magnetic field B = (3.3x10 -2) i -(3.8x10 -2) k

Force F = i ( L X B )

             = 4.5 [-2i X{(3.3x10 -2) i -(3.8x10 -2) k}]

            = 4.5 [ (-2)(3.3x10 -2) (iXi) -(-2)(3.8x10 -2) (iXk)]

            = 4.5 [ 0 +(7.6 x10 -2 ) (-j)]

            = (-0.342 j ) N

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