34. The magnetic field B can be expressed as
B(t) = B
0
+ B
1
sin(ωt + φ
0
) ,
where B
0
= (30.0 T + 29.6 T)/2 = 29.8 T and B
1
= (30.0 T
− 29.6 T)/2 = 0.200 T. Then from Eq. 31-27
E =
1
2
dB
dt
r =
r
2
d
dt
[B
0
+ B
1
sin(ωt + φ
0
)] =
1
2
B
1
ωr cos(ωt + φ
0
) .
We note that ω = 2πf and that the factor in front of the cosine is the maximum value of the field.
Consequently,
E
max
=
1
2
B
1
(2πf )r =
1
2
(0.200 T)(2π)(15 Hz)(1.6
× 10
−2
m) = 0.15 V/m .