Question

A radio wave has a maximum magnetic field induction of ${10^{ - 4}}T$ on arrival at a receiving antenna. The maximum electric field intensity of such a wave is:

Answer 1

Hint: As we know, the electric field is directly proportional to the magnetic field intensity and also proportional to the speed of the given radio wave. Speed of the light or wave is a constant value, which is $3 \times {10^8}m.{s^{ - 1}}$ .

Complete answer:
Given:
Magnetic field induction, ${B_ \circ } = {10^{ - 4}}T$
Now, we will apply the formula of maximum electric field intensity of a wave, which is directly proportional to the magnetic field induction.
$\therefore {E_ \circ } = c{B_ \circ }$
where, ${E_ \circ }$ is the electric field intensity of a wave,
and $c$ is the speed of a wave or light, and
${B_ \circ }$ is the magnetic field induction which is given already.
$\Rightarrow {E_ \circ } = (3 \times {10^8}) \times {10^{ - 4}}$
$ \Rightarrow {E_ \circ } = 3 \times {10^4}V.{m^{ - 1}}$
Hence, $3 \times {10^4}V.{m^{ - 1}}$ is the maximum electric field intensity of such a radio wave.

Additional-Information:
The electric field is the area around an electric charge where its impact can be felt. The force experienced by a unit positive charge put at a spot is the electric field intensity at that point. A positive charge's electric field intensity is always directed away from the charge, while a negative charge's intensity is always directed towards the charge.

Note:
Instead of deriving everything, the student could utilise the direct formula for electric field intensity in such a question. The electric field was assumed to be uniform in this case; however, if the field is not uniform, the answer changes. As a result, students must carefully study questions before answering them.