Question

One coulomb of point charge moving with a uniform velocity 10 x ^ m/s enters the region x ≥ 0 having a magnetic flux density B = ( 10 y x ^ + 10 x y ^ + 10 z ^ ) T . The magnitude of force on the charge at x = 0+ is ______ N. ( x ^  y ^ and z ^ are unit vectors along x-axis, y-axis, and z-axis, respectively.)

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Answer :

Given, q = 1 C

v̅ = 10 m/s

B = ( 10 y x ^ + 10 x y ^ + 10 z ^ ) T

mag = q (v̅ × B̅)

mag = 1 ( 10 x ^ × ( 10 y x ^ + 10 x y ^ + 10 z ^ ) ) N

mag = 100 x z ^ + 100 ( y ^ ) N

mag (x = 0+) = - 100 y̅ N

Magnitude of F̅mag = | ( 100 ) 2 | = 100 N

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