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 B, 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 106 ns in the region, (a) What is the magnitude of B ? (b) If the particle is sent back through the magnetic field (along the same initial path) but with 4.43 times its previous kinetic energy, how much time does it spend in the field during this trip? (a) Number Units (b) Number Units

Explanation / Answer

We know that any chargerd particles follows circu;ar path inside the magnetic field

as field is out of the page(outwards) so particle will be proton as force is toward left

radius of circle=mv/eB

time it will spend =half of time period

time period=2*pi*r/v=2*pi*m/eB

time spend=2*pi*m/2eB=pi*m/eB=106*10^(-6)

we got B=1.68*10^(-4) T=0.168 mT

(b)if kinetic energy is 4.43 times ,velocity will change but as we can see that time is independent of velocity so it will still remain same i.e.106 ns

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