#### Answer

The minimum radius is 21 cm

#### Work Step by Step

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 $F = ma$