JEE Main202430 Jan 2024Morning ShiftPhysicsElectromagnetic WavesActual
The electric field of an electromagnetic wave in free space is represented as E → = E 0 cos ( ω t - k z ) i ^ . The corresponding magnetic induction vector will be :
Options
- AB → = E 0 C cos ( ω t - k z ) j ^
- BB → = E 0 C cos ( ω t - k z ) j ^
- CB → = E 0 C cos ( ω t + k z ) j ^
- DB → = E 0 C cos ( ω t + k z ) j ^
Correct answer
B. B → = E 0 C cos ( ω t - k z ) j ^
Step-by-step solution
Given E → = E 0 cos ( ω t - k z ) i ^ : Clearly, ( ω t - k z ) term represents, electromagnetic wave is travelling along + z direction or along k ^ . Now, in vector form, direction of electromagnetive wave is given by C ^ = E ^ × B ^ . Therefore, magnetic field is along j ^ . Also, we know that B 0 = E 0 C , where C is speed of light. Therefore, B → = E 0 C cos ( ω t - k z ) j ^ .