Correct Answer - Option 1 : 0.6 N
Concept:
An electromagnetic wave consists of an electric field, defined as usual in terms of the force per charge on a stationary charge, and a magnetic field, defined in terms of the force per charge on a moving charge.
\(\vec B = {B_0}\hat i\left[ {{\rm{cos}}\left( {kz - \omega t} \right)} \right] + {B_1}{\rm{\;}}\hat j{\rm{cos}}\left( {kz + \omega t} \right)\)
Calculation:
Given,
The magnetic field is given by,
\(\vec B = {B_0}\hat i\left[ {{\rm{cos}}\left( {kz - \omega t} \right)} \right] + {B_1}{\rm{\;}}\hat j{\rm{cos}}\left( {kz + \omega t} \right)\)
Where, B0 = 3 × 10-5 T
B1 = 2 × 10-6 T
and Q = 10-4 C
\(B = \sqrt {B_0^2 + B_1^2} \)
\(B = \sqrt {{{\left( {30 \times {{10}^{ - 6}}} \right)}^2} + {{\left( {2 \times {{10}^{ - 6}}} \right)}^2}} \)
\(B = \sqrt {\left( {{{30}^2} + {2^2}} \right)} \times {10^{ - 6}}\)
B ≈ 30 × 10-6 T
The energy carried by a wave is proportional to the square of its amplitude (A2). For E&M waves, it will be (E02), or (B02), or (E0B0) where E0 and B0 are the maximum values of the electric and magnetic fields intensities.
Thus, E0 = cB
∴ E0 = cB = 3 × 108 × 30 × 10-6
= 9 × 103 V/m
Thus, the Root mean square voltage is given by,
\({{\rm{E}}_{{\rm{rms}}}} = \frac{{{E_0}}}{{\sqrt 2 }} = \frac{1}{{\sqrt 2 }} \times 9 \times {10^3}\;V/m\)
Force on the charge,
\(F = {E_{rms}}Q = \frac{9}{{\sqrt 2 }} \times {10^3} \times {10^{ - 4}} \simeq 0.64N\)
Thus, the rms value of the force experienced by the charge is 0.6 N.