Question

A plane electromagnetic wave travels in free space along \(z\)-axis. At a particular point in space, the electric field along \(x\)-axis is \(8.7 \, Vm^{-1}\). The magnetic field along \(y\)-axis is

• A. \(2.9 \times 10^{-8} \, T\)
• B. \(3 \times 10^{-6} \, T\)
• C. \(8.7 \times 10^{-6} \, T\)
• D. \(3 \times 10^{-5} \, T\)

Hint:

For an electromagnetic wave in free space, always use: \[ E=cB \] where \(c=3\times10^8 \, m/s\).

Answer 1

The Correct Option is A

Step 1: Link the two fields of an EM wave.
In a plane wave travelling through free space the field magnitudes obey \[ \frac{E}{B} = c, \] where $c = 3\times10^{8}\ \text{m s}^{-1}$ is the speed of light.
Step 2: Note the given field.
The electric field along $x$ is $E = 8.7\ \text{V m}^{-1}$.
Step 3: Rearrange for $B$.
\[ B = \frac{E}{c}. \]
Step 4: Substitute.
\[ B = \frac{8.7}{3\times10^{8}}. \]
Step 5: Evaluate.
\[ B = 2.9\times10^{-8}\ \text{T}. \]
Step 6: Check geometry and conclude.
The wave moves along $z$, $\vec{E}$ is along $x$, and $\vec{B}$ is along $y$, so the three are mutually perpendicular as required. The magnetic field is $2.9\times10^{-8}\ \text{T}$.
\[ \boxed{2.9\times10^{-8}\ \text{T}} \]