In a uniform magnetic field, an electron and a proton are orbiting in opposite d

Question

In a uniform magnetic field, an electron and a proton are orbiting in opposite directions along the same circle Perndicular to the magnetic field. A) if the speed of the electron is 3.0x10^6 m/s, what must be the speed of the proton. Assume only force on magnetic particles is magnetic force. B) if the particles are initially at the same point on the circle (moving opposite direction) where on the circle will they meet again. Answer in radian along circle In a uniform magnetic field, an electron and a proton are orbiting in opposite directions along the same circle Perndicular to the magnetic field. A) if the speed of the electron is 3.0x10^6 m/s, what must be the speed of the proton. Assume only force on magnetic particles is magnetic force. B) if the particles are initially at the same point on the circle (moving opposite direction) where on the circle will they meet again. Answer in radian along circle Perndicular to the magnetic field. A) if the speed of the electron is 3.0x10^6 m/s, what must be the speed of the proton. Assume only force on magnetic particles is magnetic force. B) if the particles are initially at the same point on the circle (moving opposite direction) where on the circle will they meet again. Answer in radian along circle

Explanation / Answer

a) F (magnetic force on a charged particle moving with velocity v) = q vB = mv^2/r

v = Bqr/ m

3 x1 0^6 = Bqr / (9.1 x 10^-31)

Bqr = ( 3 x 10^6 )( 9.1 x 10^-31) = 27.3 x 10^ -25

for proton,

Vp =  Bqr/ 1.67 x 10^-27 = ( 27.3 x 10^-25 / 1.67 x 10^-27 ) = 1.634 x 10^ 3 m/s apprx

b) VeTe = 2pir

Vp Tp = 2pir

VeTe= VpTp

Ve/ Vp = Tp/Te= 3 x1 0^6 /1.634 x 10^ 3 = 1.836 x 10^3

We= 2pi/ Te, Wp = 2pi/ Tp ( where w= rad/sec)

We/Wp = Tp/Te = 1.836 x 10^3

Angle covered by electon = 1.836x 10^3 times of proton

sum of angles = 2pi

angle covered by electron = 2pi ( 1.836 x 10^6/ 2.836 x 10^6) = 1.2947 pi

angle coverd by proton = ( 2pi - 1.2947 pi) =0.705 pi apprx

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