26. The equation of motion for the proton is

F

=

q

v

×

B = q(v

x

ˆi+ v

y

ˆj + v

z

ˆ

k)

× Bˆi = qB(v

z

ˆj

− v

y

ˆ

k)

=

m

p

a = m

p

dv

x

dt

ˆi+

dv

y

dt

ˆj +

dv

z

dt

ˆ

k

.

Thus,

dv

x

dt

=

0

dv

y

dt

=

ωv

z

dv

z

dt

=

−ωv

y

,

where ω = eB/m

p

. The solution is v

x

= v

0x

, v

y

= v

0y

cos ωt and v

z

=

−v

0y

sin ωt. In summary, we have

v(t) = v

0x

ˆi+ v

0y

cos(ωt)ˆj

− v

0y

(sin ωt)ˆ

k.