The magnetic field of an E.M. wave is given by B = ( 32 i + 12 j )30 [ (t - zc ) ] (S.I. Units). The corresponding electric field in S.I. units is:
- E = ( 12 i + 32 j )30c [ (t + zc ) ]
- E = ( 12 i - 32 j )30c [ (t - zc ) ]
- E = ( 32 i - 12 j )30c [ (t + zc ) ]
- E = ( 34 i + 14 j )30c [ (t - zc ) ]
Answer
(2) E = ( 12 i - 32 j )30c [ (t - zc ) ]
Solution
The phase (t - zc ) shows the wave travels along + k.
In an EM wave, E and B are in phase, E0 = cB0, and E B is along + k.
E = c ( B k)
i k = - j, j k = i
( 32 i + 12 j ) k = 12 i - 32 j
E = ( 12 i - 32 j )30c [ (t - zc ) ]
Check: E B 34 - 34 = 0 ✓
Answer: (2)