Answer
We can rank them in order of the radius of their paths, from largest to smallest:
$c \gt a = e \gt d \gt b \gt f$
Work Step by Step
$F = \frac{mv^2}{r}$
$F = qvB$
We can equate the two expressions for $F$ to find an expression for $r$:
$\frac{mv^2}{r} = qvB$
$r = \frac{mv}{qB}$
We can find an expression for each case:
(a) $r_a = \frac{m~(6\times 10^6)}{q~(0.3)} = (2.0 \times 10^7) \times \frac{m}{q}$
(b) $r_b = \frac{m~(3\times 10^6)}{q~(0.6)} = (5.0 \times 10^6) \times \frac{m}{q}$
(c) $r_c = \frac{m~(3\times 10^6)}{q~(0.1)} = (3.0 \times 10^7) \times \frac{m}{q}$
(d) $r_d = \frac{m~(1.5\times 10^6)}{q~(0.15)} = (1.0 \times 10^7) \times \frac{m}{q}$
(e) $r_e = \frac{m~(2\times 10^6)}{q~(0.1)} = (2.0 \times 10^7) \times \frac{m}{q}$
(f) $r_f = \frac{m~(1\times 10^6)}{q~(0.3)} = (3.3 \times 10^6) \times \frac{m}{q}$
We can rank them in order of the radius of their paths, from largest to smallest:
$c \gt a = e \gt d \gt b \gt f$
