Question

An electromagnetic wave is propagating along the X-axis. At \( x = 1 \, {cm} \) and \( t = 18 \, {s} \), its electric vector \( |E| = 8 \, {V/m} \). Then the magnitude of its magnetic vector is:

• A. \( 2.66 \times 10^{-8} \)
• B. \( 3 \times 10^{-7} \)
• C. \( 3.14 \times 10^{-8} \)
• D. \( 3.16 \times 10^{-7} \)

Hint:

In an electromagnetic wave, the magnitudes of the electric and magnetic fields are directly related to the speed of light: \( c = \frac{|E|}{|B|} \). Use this relationship to find the magnetic field given the electric field.

Answer 1

The Correct Option is A

In an electromagnetic wave, the magnitudes of the electric and magnetic fields are related by: \[ c = \frac{|E|}{|B|} \] where: - \( c = 3 \times 10^8 \, {m/s} \) (speed of light), - \( |E| = 8 \, {V/m} \) (electric field). Rearranging the formula to solve for \( |B| \), we get: \[ |B| = \frac{|E|}{c} = \frac{8}{3 \times 10^8} \] Step 1: Calculating the magnitude of the magnetic field: \[ |B| = \frac{8}{3 \times 10^8} = 2.67 \times 10^{-8} \, {T} \] This value is approximately \( 2.66 \times 10^{-8} \, {T} \). Thus, the magnitude of the magnetic field vector is \( 2.66 \times 10^{-8} \, {T} \).