In the figure, a charged particle moves into a region of uniform magnetic field

Question

In the figure, a charged particle moves into a region of uniform magnetic field Upper B Overscript right-arrow EndScripts, goes through half a circle, and then exits that region. The particle is either a proton or an electron (you must decide which). It spends 133 ns in the region. (a) What is the magnitude of Upper B Overscript right-arrow EndScripts? (b) If the particle is sent back through the magnetic field (along the same initial path) but with 3.70 times its previous kinetic energy, how much time does it spend in the field during this trip?

Explanation / Answer

magnetic force Fb = q*(v x B ) = q*v*B*sintheta

here theta = 90

Fb provides the necessary centripetal force

Fc = Fb

m*v^2/r = q*v*B

v = q*B*r/m

speed v = distance travelled/time

v = pi*r/t

pi*r/t = q*B*r/m

B = pi*m/(q*t)

m = mass of proton = 1.67*10^-27 kg

q = 1.6*10^-19 C

t = 133 ns = 133*10^-9 s

B = pi*1.67*10^-27/(1.6*10^-19*133*10^-9)

magnetic field B = 0.246 T

===================

part B

t = pi*m/(q*B)

time does not depend on speed

time remains same as 133 ns

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