An electron moves with speed 2 10^5 ~m / s along the positive x -direction in the presence of a magnetic field of induction B = i +4 j -3 k (in tesla). The magnitude of the force experienced by the electron in newtons is ( . Charge on the electron .=1.6 10⁻¹⁹ C )

Step-by-step solution

aligned & v =2 10^5 ~m / s (along X -axis) & = (2 10^4 i ) m / s & B =( i +4 j -3 k ) T & Force F =q( v B ) & For electron q=1.6 10⁻¹⁹ C & V B = | array ccc i & j & k 2 10^5 & 0 & 0 1 & 4 & -3 array | & = i [(0 -3)-(4 10)] & - j [ (2 10^5 -3 )-(1 0) ] & + k [ (2 10^5 4 )-(1 0) ] & =6 10^5 j +8 10^5 k & F =1.6 10⁻¹⁹ (6 10^5 )^2+ (8 10^5 )^2 , & =1.6 10⁻¹⁹ 10 10^5 & =1.6 10⁻¹⁸ ~N & aligned