Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation produced by a proton of mass mpmoving in a circular path perpendicular to a magnetic field of magnitude B.

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Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation produced by a proton of mass mpmoving in a circular path perpendicular to a magnetic field of magnitude B. (Use any variable or symbol stated above along with the following as necessary: q and c.)


λ = 

asked Mar 27, 2012 in Physics by yoshi ~Expert~ (919 points)
    

1 Answer

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The wavelength and frequency of electromagnetic waves are related by:

 

λ = c / f      (*where c = speed of light, f = frequency)

So to solve this equation we need to find f.

f = 1 / T           (*where T = tension)

furthermore,

T = 2*pi*R / v        (*where R = radius, v = velocity)

so now we need to solve for R and v in terms of q (charge), B (magnetic field), and m (mass of proton)

 

We do so by writing out the equation for the force of the proton we get:

q*v*B*sin(90) = m*v^2 / R         (** sin(90) goes to 1)

solving for R/v we get:

v/R = q*B / m          so            R/v = m / q*B

plugging v/R into the equation for T, we get:

T = 2*pi*m / q*B

and so 

f =  q*B /  2*pi*m

plugging this back into the equation for wavelength our final answer should be:

 

answered Mar 28, 2012 by pokemonmaster ~Expert~ (3,856 points)
edited Mar 28, 2012 by pokemonmaster

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