Section 4.1 · Worked examples · 3 of 4
Worked example 4.1.3: Under a 400 kV line
About the worked examples of Section 4.1
Four short calculations tied to the applications. They use only , its wire form and the long-wire field of Problem 4.1.1, with no new physics. Constants used: H/m ( H/m) and C. A good way to use them: read the given quantities, produce the formula from the Lorentz force or from Problem 4.1.1 yourself, and only then put the numbers in.
Under a 400 kV line
#cf. Application 4.1.3
Given. (i) One conductor of a kV line, m above the ground, carries kA. (ii) A clamp meter: a ring of mean radius cm round a cable carrying A.
Find. (a) and at the ground below, (b) the ratio to the Earth's field ( μT) and the ICNIRP level ( μT), (c) where falls to μT, (d) on the ring and the current reported.
A conductor many metres long seen from a few metres is an infinite straight wire: Problem 4.1.1 applies, , . The clamp meter is Ampère's formula made into an instrument: round the jaws equals the enclosed current, wherever the cable sits inside.
With H/m,
of the Earth's static field and of the ICNIRP 2010 public reference level at Hz. On a balanced three-phase line the three currents add to zero, so the three terms largely cancel and the real field is smaller still: the single-conductor value is an upper bound.
, so m.
On the ring, A/m, i.e. mT in air. Ampère's formula: A . The meter reports the enclosed current whatever the position of the cable in the jaws, and is blind to currents outside them. The soft-magnetic core only gathers the flux for the Hall element in its gap.
A kiloampere fifteen metres up makes a quarter of the Earth's field. The clamp meter reads , not : depends on the enclosed current alone, which is also why a cable carrying the go and return current reads zero.