An electromagnetic wave is represented by the magnetic field represented mathema

ID: 1266859 • Letter: A

Question

An electromagnetic wave is represented by the magnetic field represented mathematically by B = Bo sin [(6.591*10^8 s^-1) t + (2.198 m^-1) x]

(a) Find the frequency and wavelength of the wave

(b) Check that the speed of the wave is as expected, namely, c.

(d) If the magnetic field is vibrating north-south, how is the electric field vibrating?

(e) If Bo = 4.000*10^-9 T, find Eo, the intensity of the electric field.

(f) Find the average intensity, S, of the wave.

a)f=w/2pi =6.591*10^8/6.28 =1.036 *10^8 Hz (ans)

wavelength=2pi/k=6.28/2.198=2.857 m (ans)

b)speed,c=w/k =6.591*10^8/2.198 =2.998*10^8 m/sec (ans)

c) direction of motion =negative X direction

d)electric field vibrates perpendicular to B

EXB =C

so E X -j =-i

so E in -k direction that is negative Z direction

e)Eo =c*Bo =3*10^8 *4*10^-9 =1.2 N/C (ans)

f)average intensity =cBo^2/munot =3*10^8 *(4*10^-9)^2 /(4*3.14*10^-7)=3.82*10^-3 W/m^2 (ans)

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