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 .