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 $F = ma$
