Additional Materials Section 214SolutionThe magnetic field B

Additional Materials

Section 21.4

Solution

The magnetic field B creates a force on a moving charge such that F = q*v*B

Now this causes a centripetal acceleration = m*v^2/r

so q*v*B = m*v^2/r

or B = m*v/(r*q)

If the accelerating potential V is the same then the kinetic energy =1/2*m*v^2 equals the potential energy difference

so 1/2*m*v^2 = V*q

so the speed v = sqrt(2*V*q/m)

so now B = m*sqrt(2*V*q/m)/(r*q) simplifying we get

B = sqrt(2*V*m/q)/r

now in your problem you want r to be the same given that q and V are the same

So B7 = sqrt(m7)*sqrt(2*V/q)/r

I\'ve written it is this form to show that for the \\given conditions B is a function of sqrt(m)

So Now B10/B7 = sqrt(m10/m7)

so B10 = B7*sqrt(m10/m7) = 0.3362T*sqrt(1.663x10^-26/1.165x10^-26) = 0.4061T