## College Physics (4th Edition)

We can use Newton's second law to find an expression for the force required to make an object move in a circle: $F = ma$ $F = m~\frac{v^2}{r}$ We can write an expression for the magnetic force: $F = qvB$ We can equate the two expressions for $F$ to find the minimum required value for $r$: $\frac{mv^2}{r} = qvB$ $r = \frac{mv}{qB}$ $r = \frac{(1.67\times 10^{-27}~kg)(3.0\times 10^7~m/s)}{(1.6\times 10^{-19}~C)(1.5~T)}$ $r = 0.21~m$ The minimum radius is 21 cm We can see that this result comes from Newton's second law $F = ma$