Magnetism and Centripetal force question

[jumpfreak]

Homework Statement

One method for determing masses of heavy ions involves timing their orbital period in a known magnetic field. What is the mass of a singly charged ion that makes 7.0 revolutions in 1.3 x 10^-3 seconds in a 4.5 x 10^-2 T field.

a) 2.1x10^-25 kg
b) 1.3x10^-24 kg
c) 6.5x10^-23 kg
a) 5.0x10^-20 kg

Homework Equations

I'm not sure of which equation to use. Maybe...
Fc = Fb
m4(pi^2)r/T^2 = QvB

The Attempt at a Solution

m4(pi^2)r/(1.3x10^-3s/7)^2 = Qv(4.5x10^-2)

This might be the wrong formula.

 

[Andrew Mason]

Homework Statement

One method for determing masses of heavy ions involves timing their orbital period in a known magnetic field. What is the mass of a singly charged ion that makes 7.0 revolutions in 1.3 x 10^-3 seconds in a 4.5 x 10^-2 T field.

a) 2.1x10^-25 kg
b) 1.3x10^-24 kg
c) 6.5x10^-23 kg
a) 5.0x10^-20 kg

Homework Equations

I'm not sure of which equation to use. Maybe...
Fc = Fb
m4(pi^2)r/T^2 = QvB

The Attempt at a Solution

m4(pi^2)r/(1.3x10^-3s/7)^2 = Qv(4.5x10^-2)

This might be the wrong formula.

It is the right formula.

If $mv^2/r = qvB$ where $v = 2\pi r/T$ then:

$$qB = m2\pi/T$$

$$m = qBT/2\pi$$

Just plug in the numbers.

AM

 

[jackiefrost]

One caution:

In the previously cited equation $$m = qBT/2\pi$$, T is the orbital period = (1.3 x 10^-3)/7 sec