Question

Electromagnetic radiations are emitted from a \(15\,\text{W}\) point source. The peak value of the magnetic field at a distance of \(5\,\text{m}\) from the source is

• A. \(4\times10^{-8}\,\text{T}\)
• B. \(2\times10^{-8}\,\text{T}\)
• C. \(2\times10^{-7}\,\text{T}\)
• D. \(4\times10^{-7}\,\text{T}\) \bigskip

Hint:

For an isotropic source, \[ I=\frac{P}{4\pi r^2}. \] For an electromagnetic wave, \[ I=\frac{c}{2\mu_0}B_0^2 \] and \[ E_0=cB_0. \] These relations allow direct calculation of the peak electric or magnetic field from the power of the source.

Answer 1

The Correct Option is B

Concept: Intensity \(I = P/(4\pi r^2) = (c/2\mu_0)B_0^2\). Solve for \(B_0\).

Step 1: \(I = 15/(4\pi\cdot25) = 15/(100\pi) \approx 4.77\times10^{-2}\) W/m². \(B_0 = \sqrt{2\mu_0 I/c} = \sqrt{2\cdot4\pi\times10^{-7}\cdot4.77\times10^{-2} / 3\times10^8} \approx 2\times10^{-8}\) T.

Step 2: Write the final answer. \(\boxed{B_0=2\times10^{-8}\,\text{T}}\)