Electric and Magnetic fields at one point on an electromagnetic wave

[mateo710]

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are
E = (210 + 320 − 40) V/m and B = B0(7.5 − 7.5 + a) μT. Find a and B0



E=cB

The Attempt at a Solution

So I found a using E dot product B = 0 and I got the value a=-20.625 and this is correct.

Next I tried find B0 using E=cB. Using only the i components, 210=(c)(B0)(7.5E-6) I got the answer B0=.0933 but smartphysics won't accept this.

Am I missing something? Also why do I use the i component, which is related to the direction of the wave, rather than using the k component, which is related to the magnetic field?

Thanks in advance

 

[jbsteele]

.To find B0, you need to use the magnitude of the electric and magnetic fields, not just the i-component. You can use either the magnitude of E or B, since they are related by c. In this case, it would be:E = (210 + 320 − 40) V/m = 490 V/mB = B0(7.5 − 7.5 + a) μT = B0(-20.625) μTSo, B0 = 490/(-20.625*10^-6) = -2.37 x 10^-4 T.