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Question:

A monochromatic beam of light has a frequency v = 32π × 1012 Hz and is propagating along the direction ^i + ^j/√2. It is polarized along the ^k direction. The acceptable form for the magnetic field is:

E0C(^i − ^j/√2)cos[104(^i + ^j/√2) ⋅ ^r − (3 × 1012)t]

E0C^kcos[104(^i + ^j/√2) ⋅ ^r + (3 × 1012)t]

^kE0C(^i − ^j/√2)cos[104(^i − ^j/√2) ⋅ ^r − (3 × 1012)t]

E0C(^i + ^j + ^k)√3cos[104(^i + ^j/√2) ⋅ ^r + (3 × 1012)t]

Solution:

Direction of B is ,=^K × ^E = (^i + ^j/√2) × ^K = ^i × ^K/√2 + ^j × ^K/√2 = ^j/√2 − ^i/√2 = ^i − ^j/√2
So, ans is between (i) and (iii)
Propagation direction ,^k = ^i + ^j/√2
^B wave eqn will be
→E0c(^B)Cos[|k|^k − wt]
↓ ↓
we know it is ^i − ^j/√2 ^i + ^j/√2
Only (iii) satisfies
Hence , correct answer is (iii)