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Question

An element dl=dx icap is placed at the origin and carries a large current I =10A .What is the magnetic field on the y-axis at a distance of 0.5m .dx =1cm?


Solution

 dℓ = dx = 10–2 m

                              I = 10A

                              r = 0.5 m

                    dB = (μ0 / 4π)[(I dℓ × r) / r3] = [(μ0 I dℓ sinθ) / (4π × r2)]

                      ∴ magnetic field on y axis = [(4π × 10–7) / 4π] × [(10 × 10–2) / (0.5)2]

                                                            = [(10)–8 / (25 ×10–2)] = 0.04 × 10–6

                                                            = 4 × 10–8 T

                    i.e.      dB = 4 × 108 k˄ T (y axis)

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