Answer:
[tex]v_{y} = -104 m/s[/tex]
Explanation:
Using:
Force = electric field * charge
[tex]F=e*q[/tex]
Force = magnitude of charge * velocity * magnetic field * sin tither
[tex]F_{x2}= |q|*v*B*sin \alpha[/tex]
Force on particle due to electric field:
[tex]F_{x1}= E*q = (1270N/C)*(-6.72*10^{-6} ) = -8.53*10^{-3}[/tex]
Force on particle due to magnetic field:
[tex]F_{x2}= |q|*v*B*sin \alpha = (6.72*10^{-6} )*(1.15)*(sin90)*v = (7.728*10^{-6})*(v)[/tex]
[tex]F_{x2}[/tex] is in the positive x direction as [tex]F_{x1}[/tex] is in the negative x direction while net force is in the positive x direction.
Magnetic field is in the positive Z direction, net force is in the positive x direction.
According to right hand rule, Force acting on particle is perpendicular to the direction of magnetic field and velocity of particle. This would mean the force is along the y-axis. As this is a negatively charged particle, the direction of the velocity of the particle is reversed. Therefore velocity of particle, v, has to be in the negative y direction.
Now,
[tex]F_{xnet}- F_{x1 } = F_{x2 }[/tex]
[tex](6.13*10^{-3}) - (8.53*10^{-3} ) = (7.728*10^{-6})*(v)[/tex]
[tex]v = (F_{xnet} - F_{x1}) / (F_{x2} )[/tex]
[tex]=((6.13*10^{-3} ) - (8.53*10^{-3})) / (7.728*10^{-6})[/tex]
[tex]= (- 104.25) m/s[/tex]
[tex]v_{y} = -104 m/s[/tex]
