Question
In an electromagnetic wave in free space the root mean square value of the electric field is $${E_{{\text{rms}}}} = 6\,V/m.$$ The peak value of the magnetic field is
A.
$$1.41 \times {10^{ - 8}}T$$
B.
$$2.83 \times {10^{ - 8}}T$$
C.
$$0.70 \times {10^{ - 8}}T$$
D.
$$4.23 \times {10^{ - 8}}T$$
Answer :
$$2.83 \times {10^{ - 8}}T$$
Solution :
Given, root mean square value of electric field,
$${E_{rms}} = 6\;V/m$$
We know that, peak value of electric field,
$$\eqalign{
& {E_0} = \sqrt 2 {E_{rms}} \cr
& \Rightarrow {E_0} = \sqrt 2 \times 6\;V/m \cr} $$
Also, we know that, $$c = \frac{{{E_0}}}{{{B_0}}}$$
where, $$c =$$ speed of light in vacuum
$${B_0} =$$ peak value of magnetic field
$$\eqalign{
& \Rightarrow {B_0} = \frac{{{E_0}}}{c} \Rightarrow {B_0} = \frac{{\sqrt 2 \times 6}}{{3 \times {{10}^8}}} \cr
& \Rightarrow {B_0} = \frac{{8.48}}{3} \times {10^{ - 8}} \Rightarrow {B_0} = 2.83 \times {10^{ - 8}}\;T \cr} $$