Question

If the magnetic field of an electromagnetic wave is given as $B_y=2\times {10}^{-7}\sin ({10}^{3}x+1.5\times {10}^{12}t)$ tesla, the wavelength of the electromagnetic wave is

• A. $0.314mm$
• B. $0.628mm$
• C. $6.28mm$
• D. $1.26mm$
• E. $0.0628mm$

Answer 1

The correct option is C $6.28mm$

The general equation of an electromagnetic wave is $B=A\sin (kx+\omega t)$

Comparing this equation with the given equation, $A=2\times {10}^{-7}$, $k={10}^3$ and $\omega =1.5\times {10}^{12}$

We know that , wave number $k=\frac{2\pi }{\lambda }$

So, ${10}^3=\frac{2\pi }{\lambda }$

or $\lambda =6.28\times {10}^{-3}m=6.28mm$