Question

Lightning bolts can carry currents up to approximately 20 kA . We can model such a current as the equivalent of a very long, straight wire. (a) If you were unfortunate enough to be 5m away from such a lightning bolt, how large a magnetic field would you experience? (b) How does this field compare to one you would experience by being 5cm from a long, straight household current of 10A ?

Short answer

a)$B=8\times {10}^{-4}T$

b)$B=4\times {10}^{-5}T$

Step-by-step solution

Take lightening as a very long wire

To simplify the calculations, we will take lightening as a very long wire. The formula of magnetic field will become$\mathit{B}\mathbf{=}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{I}}{\mathbf{2}\mathbf{\pi r}}$ .

Given that$I=20kA$ and r = 5m .

$\begin{array}{r}B=\frac{{\mu }_{0}I}{2\pi r}\\ B=\frac{4\pi \times {10}^{-7}\times 20000}{2\pi \times 5}\\ B=8\times {10}^{-4}T\end{array}$

Calculate the magnetic field for the second case

In the second case, r = 5 cm and I = 10 A .

$\begin{array}{r}B=\frac{4\pi \times {10}^{-7}\times 10}{2\pi \times 5\times {10}^{-2}}\\ B=4\times {10}^{-5}\mathrm{T}\end{array}$

We can see that field due to lightening bolt is about twenty times as strong as the field due to the household.