## College Physics (4th Edition)

We can rank them in order of the radius of their paths, from largest to smallest: $c \gt a = e \gt d \gt b \gt f$
$F = \frac{mv^2}{r}$ $F = qvB$ 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: $c \gt a = e \gt d \gt b \gt f$