The Electromagnetic Balance Scale · AI Generator #GEN-EA0767C4

Physics · electromagnetism

Problem

A sensitive analytical balance uses electromagnetic forces instead of mechanical springs. The device consists of two identical circular coils of radius

R = 2.0\;\text{cm}

with

N = 100

turns each, positioned vertically with their axes aligned. The lower coil is fixed, while the upper coil (mass

m = 15\;\text{g}

) can move vertically and is suspended by a thin non-magnetic thread. When both coils carry the same current

I

in the same direction, the magnetic force between them exactly balances the weight of the upper coil, keeping it suspended at a separation distance

d = 1.5\;\text{cm}

between their centers. To weigh a small sample, the sample is attached to the upper coil, and the current is adjusted until the coil returns to the same equilibrium position

d = 1.5\;\text{cm}

. When a sample of mass

m_s = 2.0\;\text{g}

is attached, the required current becomes

I_2 = 1.2\;\text{A}

. Find the original current

I_1

needed to suspend the empty upper coil. Use

\mu_0 = 4\pi \times 10^{-7}\;\text{H/m}

and

g = 9.8\;\text{m/s}^2

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