a)If a charged particle is undeflected in passing through uniform crossed electr

Question

a)If a charged particle is undeflected in passing through uniform crossed electric and magnetic fields E and B (mutually perpendicular and both perpendicular to the direction of motion), what is its velocity? (Express your answer in terms of E, and B.) b) If we now turn of the electric field, and the particle moved in an arc R what is its charge-to-mass ratio? (Express you answer in terms of E, B and R.) c) Write an expression for the momentum of the particle in terms of q (charge), B, and R. d) Assume the three charged particles shown are “fragments” of the decay of heavier particle traveling to the right with an initial momentum of 5.36 x 10-22 kg-m/s. They are bending in uniform magnetic field. If the radius of curvature R1 = 2.5 cm and the radius of curvature R2 = 1.7 cm, what is the radius R3? Assume each fragment particle carries the fundamental charge and has the mass of an electron and B = 1 T. e) Assume the B field points into the page. What is the charge sign on each particle?

Explanation / Answer

a)

V = speed of charge

E = electric field

B = magnetic field

for charge to pass undeflected

magnetic force = electric force

qVB = qE

V = E/B

b)

R = Radius of arc

In magnetic field , radius of arc is given as

R = mV/qB

q/m = V/RB = (E/B) / (RB) = E / (R B2)

c)

momentum is given as

P = mV = qBR

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