Question

Intensity of sunlight is observed as $0.092{\text{Wm}}^{-2}$ at a point in free space. What will be the peak value of magnetic field at that point ?
$({\epsilon }_0=8.85\times {10}^{-12}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2})$

• A. $8.31\text{T}$
• B. $5.88\text{T}$
• C. $2.77\times {10}^{-8}\text{T}$
• D. $1.96\times {10}^{-8}\text{T}$

Answer 1

The correct option is C $2.77\times {10}^{-8}\text{T}$

If $B_0$ is the peak value of magnetic field and $c$ is the velocity of light in free space, then the intensity is given by,

$I=\frac{B_0^{2}c}{2{\mu }_0}$ and $\frac{1}{{\mu }_0}={\epsilon }_0{c}^2$

$\Rightarrow I=\frac{B_0^2}{2}{\epsilon }_0{c}^3$

$\Rightarrow B_0=\sqrt{\frac{2I}{{\epsilon }_0{c}^3}}$

$\Rightarrow B_0=\sqrt{\frac{2\times 0.092}{(8.85\times {10}^{-12})(3\times {10}^8{)}^3}}$

$\Rightarrow B_0=2.77\times {10}^{-8}\text{T}$

Hence, $\left(A\right)$ is the correct answer.