Physics : A proton (Charge= +e, mass=M) and a deuteron (charge = +e, mass = 2M)...
Physics :
A proton (Charge= +e, mass=M) and a deuteron (charge = +e, mass = 2M) have the same kinnetic energy. They enter a magnetic field and both move in circular paths. How are the radii of the paths Rp and Rd related?
A.) Rd = Rp
B.) Rd = 2Rp
C.). Rd = sqrt(2Rp)
D.) Rd = Rp/2
E.) Rd = Rp / sqrt(2)
Homework Answers
E) Rd = Rp / sqrt(2)
we know,
radius of orbit, r = m*v/(B*q)
= sqrt(2*m*KE)/(B*q)
let KE is kinetic energy of the two particles.
so,
Rp = sqrt(2*M*KE)/(B*e)
Rd = sqrt(2*2*M*KE)/(B*2*e)
take the ration,
Rd/Rp = ( sqrt(2*2*M*KE)/(B*2*e) )/(sqrt(2*M*KE)/(B*e) )
Rd/RP = sqrt(2)/2
Rd/RP = 1/sqrt(2)
Rd = Rp/sqrt(2)
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