Question

A plane electromagnetic wave with frequency \(40\,\text{MHz}\) travels in free space. At a particular point in space and time, the magnetic field is \(2 \times 10^{-8}\,\text{T}\). What will be the electric field at this point?

• A. \(16\,\text{V m}^{-1}\)
• B. \(6\,\text{V m}^{-1}\)
• C. \(8\,\text{V m}^{-1}\)
• D. \(18\,\text{V m}^{-1}\)

Hint:

In free space, electric and magnetic fields in EM waves are related by \(E = cB\), independent of frequency.

Answer 1

The Correct Option is B

Step 1: Use relation between electric and magnetic fields.
For an electromagnetic wave in free space:
\[ E = cB \]
where \(c = 3 \times 10^8\,\text{m/s}\).

Step 2: Substitute given values.
\[ B = 2 \times 10^{-8}\,\text{T} \]
\[ E = 3 \times 10^8 \times 2 \times 10^{-8} \]

Step 3: Simplify the expression.
\[ E = 6 \times 10^0 \]
\[ E = 6\,\text{V m}^{-1} \]

Step 4: Note about frequency.
The frequency \(40\,\text{MHz}\) is not required here since the relation \(E = cB\) holds for all EM waves in free space.

Step 5: Final answer.
\[ \boxed{6\,\text{V m}^{-1}} \]