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Equation 2 · The Last Artefact: Redefining the Kilogram

What does this equation mean?

mxg=I1BlandU2=vBlm_x g = I_1 B l \qquad\text{and}\qquad U_2 = v B l

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationsI_1 B l qquadandqquad U_2 = v B l
Result or conditionm_x g
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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mxm_x

Symbol m_x

mxm_x is part of the quantity the equation computes from the expression on the right.

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gg

Symbol g

g is part of the quantity the equation computes from the expression on the right.

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I1I_1

Symbol I_1

I1I_1 is an input to the expression that computes the quantity on the left.

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BB

Symbol B

B is an input to the expression that computes the quantity on the left.

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ll

Symbol l

l is an input to the expression that computes the quantity on the left.

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U2U_2

Symbol U_2

U2U_2 is an input to the expression that computes the quantity on the left.

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vv

Symbol v

the velocity.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

The Kibble balance runs in two modes. In weighing mode, the weight of an artefact of mass m is balanced by the force on a coil of wire length l carrying current I₁ in a radial field of flux density B. In moving mode, the same coil is driven vertically at velocity v through the same field and the induced voltage U₂ is measured [ 4 ] : mxg=I1BlandU2=vBlm_x g = I_1 B l \qquad\text{and}\qquad U_2 = v B l. The geometric factor Bl appears in both and is eliminated between them:

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Sources cited in the surrounding passage

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