A charged particle enters a velocity selector with a speed of 6.00 times 10^4 m/

Question

A charged particle enters a velocity selector with a speed of 6.00 times 10^4 m/s. The geometry of the velocity selector is similar to that shown below, with the initial velocity of the particle directed parallel to the plates of the velocity selector, and perpendicular to both the electric field and the magnetic field, which are perpendicular to one another. There is a uniform magnetic field, directed perpendicular to the page, between the plates. A graph of the net force acting on the particle when it enters the velocity selector, as a function of the magnetic filed in the velocity selector, is shown below. A positive net force means that the particle is deflected up, while a negative net force means that it is deflected down. Neglect any gravitational interactions. Using the graph, determine the magnitude of the electric field in the velocity selector. Using the graph, determine the magnitude of the charge on the particle.

Explanation / Answer

(a)

Magnitude of Electric Field = E

F = qE

F = Bqv

qE = Bqv

E = Bv

B from graph is 0.5 T and v is given 6 x 104

so,

E = 3 x 104 N/C

(b)

Magnitude of charge on particle

q = F/E

q = 3 x 10-3/3 x 104

q = 10 C

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