TS EAMCET 18-July-2022 Shift 2 Solved Paper

Equations of EM waves are given as,
‌E(t)=Emsin‌(kx−ωt)
‌B(t)=Bmsin‌(kx−ωt)
If ‌

^

x

and ‌

^

y

are unit vectors along E(t) and B(t) respectively, then
‌‌

^

x

=‌

‌ ^ i +‌ ^ j

√12+12

=‌

‌ ^ i +‌ ^ j

√2

‌‌

^

y

=‌

‌ ^ i −‌ ^ j

√12+12

=‌

‌ ^ i −‌ ^ j

√2

∴ Unit vector in the direction of propagation of EM wave is ‌

^

z

, then
‌

^

z

‌=‌

^

x

×‌

^

y

‌=(‌

‌ ^ i +‌ ^ j

√2

)×(‌

‌ ^ i −‌ ^ j

√2

)
‌=‌

1

2

[‌

^

i

×‌

^

i

−‌

^

i

×‌

^

j

+‌

^

j

×‌

^

i

−‌

^

j

×‌

^

j

]
‌=‌

1

2

[0−‌

^

k

−‌

^

k

−0]=‌

1

2

×(−2‌

^

k

)=−‌

^

k

Hence, unit vector along the direction of propagation of EM wave will be −‌

^

k

.