# 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.

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

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