# Thread: Deriving a formula for magnetic

1. ## Deriving a formula for magnetic

Hello, it says that we must derive m = qB^2r^2/2V ..(volts)
using formula for kinetic energy and E= kq/r^2

thanks in advance for the help

2. Originally Posted by joeblack437
Hello, it says that we must derive m = qB^2r^2/2V ..(volts)
using formula for kinetic energy and E= kq/r^2

thanks in advance for the help
I can't make sense of your question. Is the charge in a magnetic field? Electric field? Both? What sort of fields? Constant?

Give all the of the question.

3. A mass spectometer accelerates ions through a voltage, V, before the ions enter a uniform magnetic field, B, that makes them turn. Develop the forumla m= qB^2r^2/2V for the mass of the ion, using kinetic and charge energy. the radius of the turn is r and the charge is q

4. Originally Posted by joeblack437
A mass spectometer accelerates ions through a voltage, V, before the ions enter a uniform magnetic field, B, that makes them turn. Develop the forumla m= qB^2r^2/2V for the mass of the ion, using kinetic and charge energy. the radius of the turn is r and the charge is q
K.E. = qV when ion enters magnetic field: $\displaystyle \frac{mv^2}{2} = qV$

$\displaystyle \Rightarrow mv^2 = 2 q V$ .... (1)

In magnetic field: $\displaystyle F = \frac{mv^2}{r} = q v B \Rightarrow mv = r q B$

$\displaystyle \Rightarrow v^2 = \frac{r^2 q^2 B^2}{m^2}$ .... (2)

Substitute (2) into (1): $\displaystyle \frac{r^2 q^2 B^2}{m} = 2 q V$

and I'm sure you can make m the subject and simplify.