A particle with charge q and kinetic energy K travels in a uniform magnetic field of magnitude B. If the particle moves in a circular path of radius R, find expressions for each of the following

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A particle with charge q and kinetic energy K travels in a uniform magnetic field of magnitude B. If the particle moves in a circular path of radius R, find expressions for each of the following. (Use any variable or symbol stated above as necessary.)

 

(a) its speed
v =  

(b) its mass
m = 
asked Feb 10, 2012 in Physics by Joey33 ~Expert~ (1,216 points)
    

2 Answers

+6 votes
 
Best answer
Start by writing the equation for magnetic force:

magnetic force = q*v*B

Now write the equation for centripetal acceleration:

a = v^2 / R

Force = m*a

plugging in a we get:

Force = m* v^2 / R

Now set magnetic force equal to force:

q*v*B  = m* v^2 / R

 

Now we need to use K.

K = (1/2)m*v^2

multiplying by 2 this becomes:

2K = m*v^2  , which we can now subsitute into the equation above and get:

q*v*B  = 2K / R

Solving for v we get:

v = 2K/ (R*q*B)

 

Part B, similarly we can calculate mass by using the force equation again:

Force = m*a

and so solving for m we get:

m = Force / a

Where Force = q*v*B furthermore the v can be replaced for what we got in part A.

so Force = q*(2K/ (R*q*B))*B

and a = v^2 / R, furthermore the v can be replaced for what we got in part A.

so a =  (2K/ (R*q*B))^2) / R

 

plugging into the equation for m we get:

m = *q*(2K/ (R*q*B))*B) / (2K/ (R*q*B))^2) / R

after simplifying we get that:

m = (R*q*B)^2 / (2K)
answered Feb 18, 2012 by pokemonmaster ~Expert~ (3,856 points)
selected Feb 18, 2012 by Joey33
+4 votes
a) v=2K/(RqB)

 
b) (RqB)^2/2K
answered Feb 15, 2012 by joshuamcelwain ~Rookie~ (80 points)

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