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A particle of mass 0.2g carries a charge 10^-8C. It was given an initial horizontal velocity...

A particle of mass 0.2g carries a charge 10^-8C. It was given an initial horizontal velocity ?? = (5 × 10^4 ??) in +x direction. What are the magnitude and direction of the minimum magnetic field that will cancel gravitational effects? Neglect Earth’s magnetic field.

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Answer #1

gravitational force acts down wards -z direction


gravitational force Fg = m*g (-k)

magnetic force = Fb


Fb + Fg = 0


Fb = -Fg

magnetic force Fb must act along +z direction ( upward)

magnetic force Fb = q*( V X B ) k


B = Bxi + Byj + Bzk

Fb = q*( vxi X (Bxi + Byj + Bzk )


Fb = q*vx*By ( i X j ) + q*vx*Bz ( i X k )

Fb = q*vx*By k - q*vx*Bz j


Fb is along +K


magnitude of Fb

Fb = q*vx*By

magnetic field is along +y direction


Fb = Fg

q*Vx*By = m*g


10^-8*5*10^4*By = 0.2*10^-3*9.8


minimum magnetic field By = 3.92 T

magnetic field is along +y direction

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