In the figure, an electron with an initial kinetic energy of 3.60 keV enters reg

Question

In the figure, an electron with an initial kinetic energy of 3.60 keV enters region 1 at time t = 0. That region contains a uniform magnetic field directed into the page, with magnitude 0.00590 T. The electron goes through a half-circle and then exits region 1, headed toward region 2 across a gap of 23.0 cm. There is an electric potential difference V = 2000 V across the gap, with a polarity such that the electron's speed increases uniformly as it traverses the gap. Region 2 contains a uniform magnetic field directed out of the page, with magnitude 0.0209 T. The electron goes through a half-circle and then leaves region 2. At what time t does it leave?

Explanation / Answer

at region 1,

t1=pi*m/q*B1

t1=pi*9.1*10^-31/(1.6*10^-19*0.0059)

t1=3.03*10^-9 sec

at region 2,

t2=pi*m/q*B2

t2=pi*9.1*10^-31/(1.6*10^-19*0.0209)

t2=8.55*10^-10 sec

and

in between gap,

F*d=q*V

m*a*d=q*V

m*a*d=1.6*10^-19*2000

9.1*10^-31*a*23*10^-2=1.6*10^-19*2000

====> a=1.53*10^15 m/sec^2

and

K.E=1/2*m*u^2

3.6*1.6*10^-19*10^3=1/2*9.1*10^-31*u^2

===> u=3.56*10^7 m/sec

now,

d=u*t3+1/2*a*t3^2

23*10^-2=3.56*10^7*t3+1/2*1.53*10^15*t3^2

===> t3=5.23*10^-8 sec

total time taken, T=t1+t2+t3

T=3.03*10^-9+8.55*10^-10+5.23*10^-8

T=5.62*10^-8 sec

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