Rank the magnitudes of the forces exerted on the following particles from larges

Question

Rank the magnitudes of the forces exerted on the following particles from largest to smallest. In your ranking, display any cases of equality. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) (a) an electron moving at 1 Mm/s perpendicular to a 1-mT magnetic field (b) an electron moving at 1 Mm/s parallel to a 1-mT magnetic field (c) an electron moving at 2 Mm/s perpendicular to a 1-mT magnetic field (d) a proton moving at 1 Mm/s perpendicular to a 1-mT magnetic field (e) a proton moving at 1 Mm/s at a 45° angle to a 1-mT magnetic field

Explanation / Answer

we know force acting on moving charge, f = q*v*B*sin(theta).

so,

Fa = q*v*B*sin(90) = 1.6*10^-19*1*10^6*1*10^-3*1 = 1.6*10^-16 N

Fb = q*v*B*sin(0) = 0

Fc = q*v*B*sin(90) = 1.6*10^-19*2*10^6*1*10^-3*1 = 3.2*10^-16 N

Fd = q*v*B*sin(90) = 1.6*10^-19*1*10^6*1*10^-3*1 = 1.6*10^-16 N

Fe = q*v*B*sin(45) = 1.6*10^-19*1*10^6*1*10^-3*sin(45) = 1.13*10^-16 N

so,

Fc > Fa = Fd > Fe > Fb

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