Answer:
The z-component of the force is [tex]\= F_z = 0.00141 \ N[/tex]
Explanation:
From the question we are told that
The charge on the particle is [tex]q = 7.76 *0^{-8} \ C[/tex]
The magnitude of the magnetic field is [tex]B = 0.700\r i \ T[/tex]
The velocity of the particle toward the x-direction is [tex]v_x = -1.68*10^{4}\r i \ m/s[/tex]
The velocity of the particle toward the y-direction is
[tex]v_y = -2.61*10^{4}\ \r j \ m/s[/tex]
The velocity of the particle toward the z-direction is
[tex]v_y = -5.85*10^{4}\ \r k \ m/s[/tex]
Generally the force on this particle is mathematically represented as
[tex]\= F = q (\= v X \= B )[/tex]
So we have
[tex]\= F = q ( v_x \r i + v_y \r j + v_z \r k ) \ \ X \ ( \= B i)[/tex]
[tex]\= F = q (v_y B(-\r k) + v_z B\r j)[/tex]
substituting values
[tex]\= F = (7.7 *10^{-8})([ (-2.61*10^{4}) (0.700)](-\r z) + [(5.58*10^{4}) (0.700)]\r y)[/tex]
[tex]\= F= 0.00303\ \r j +0.00141\ \r k[/tex]
So the z-component of the force is [tex]\= F_z = 0.00141 \ N[/tex]
Note : The cross-multiplication template of unit vectors is shown on the first uploaded image ( From Wikibooks ).
