1)What magnitude of transverse magnetic fieldwould be required for protons of ve

Question

1)What magnitude of transverse magnetic fieldwould be required for protons of velocity 2.0 ×105 m/s to move in acyclotron orbit of radius 20 cm? (Ans: 1.0 x 10^ -2T ) 2) An FM radio station broadcastselectromagnetic waves at a frequency of 100. 1 MHz. The amplitudeof the electric field is 4.0 × 10-3 V/m.
(a) What is the wavelength? (Ans: 3.0 m) (b) What is the amplitude of the magneticfield? (Ans: 1.3 x10^ -11 T) 1)What magnitude of transverse magnetic fieldwould be required for protons of velocity 2.0 ×105 m/s to move in acyclotron orbit of radius 20 cm? (Ans: 1.0 x 10^ -2T ) 2) An FM radio station broadcastselectromagnetic waves at a frequency of 100. 1 MHz. The amplitudeof the electric field is 4.0 × 10-3 V/m.
(a) What is the wavelength? (Ans: 3.0 m) (b) What is the amplitude of the magneticfield? (Ans: 1.3 x10^ -11 T) (b) What is the amplitude of the magneticfield? (Ans: 1.3 x10^ -11 T)

Explanation / Answer

velocity of proton v = 2*105  m/s    radius of the orbit r = 20 cm = 0.2m       mass of proton m =1.6*10-27 kg    charge on proton q =1.6*10-19 C       magnetic force on proton F = B q v       proton move incyclotron orbit . so the force is centripetalforce       m v 2  / r = B q v magnitude of magnetic field B = m v / q r          =( 1.6*10-27 kg)(2*105  m/s ) / ( 1.6*10-19 C )( 0.2 )          =10*10-3 T             =1*10-2 T The relation between frequency and wave length is      f = c /    here c = velocity ofslight = 3*108 m/ s    wavelength of the wave = v / f = 3*108  m/s / 100.1 *106                   = 3 m         

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