Question

An electromagnetic wave has frequency \(50\,MHz\) and electric field amplitude \(5.6\,V\,m^{-1}\). Find the magnetic field amplitude.

• A. \(1.9\times10^{-8}\,T\)
• B. \(1.8\times10^{-8}\,T\)
• C. \(2.0\times10^{-8}\,T\)
• D. \(5.6\times10^{-8}\,T\)

Hint:

For electromagnetic waves, \[ E_0=cB_0. \] The electric and magnetic fields are always perpendicular to each other and to the direction of propagation.

Answer 1

The Correct Option is A

Concept: For an electromagnetic wave, \[ E_0=cB_0 \] where \[ E_0=\text{electric field amplitude}, \] \[ B_0=\text{magnetic field amplitude}, \] and \[ c=3\times10^8\,m\,s^{-1}. \]

Step 1: Write the given values. \[ E_0=5.6\,V\,m^{-1} \] \[ c=3\times10^8\,m\,s^{-1} \]

Step 2: Use the relation between electric and magnetic fields. \[ B_0=\frac{E_0}{c} \] Substituting the values, \[ B_0=\frac{5.6}{3\times10^8} \] \[ B_0=1.867\times10^{-8}\,T \]

Step 3: Round to the nearest option. \[ B_0\approx1.9\times10^{-8}\,T \]

Step 4: Final answer. \[ \boxed{1.9\times10^{-8}\,T} \] Hence, \[ \boxed{(A)} \]