A charged particle of charge q and mass m starts at rest and is accelerated thro

Question

A charged particle of charge q and mass m starts at rest and is accelerated through a potential difference delta V applied across two parallel plates separated by a distance S. It then enters a region of unifrom magnetic field (pointing out of the paper) where its moves at a speed v and its trajectory becomes circular. After following a half-circle of diameter d, it passes through a small opening and hits a detector. Is the sign of the particles charge positive or negative? Between the plates what direction is the electric field pointing? What is the acceleration of particle while it is between the plates? Your answer should be in terms of some or all of the following variables: q, m, delta V, S, d, and B. What is the acceleration of particle while it is traveling in the magnetic field? Your answer should be in terms of some or all of the following variables: q, m, delta V, S, d, and B.

Explanation / Answer

a) positive charge

b) from left to right

c) F = q*E = m*a

accelaration a = q*E/m = (q*dV)/(m*S)

d) magnetic Force = F = q*v*B = m*a

accelaration a = q*v*B/m

where v is the speed of the particle while enteriong into the field

q*dV = 0.5*m*v^2

v= sqrt(2*q*dV/m)

then a = q*sqrt(2*q*dV/m)*B/m

a = sqrt(2*dV)*q^(3/2)*B / m^(3/2)

a= sqrt(2*dV)*(q/m)^(3/2)*B

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