A current balance is a device to measure magnetic forces. It is constructed from two parallel coils, each with an average radius of 12.5 cm. The lower coil rests on a balance; it has 20 turns and carries a constant current of 1.30 A. The upper coil, suspended 0.314 cm above the lower coil, has 50 turns and a current that can be varied. The reading of the balance changes as the magnetic force on the lower coil changes. What current is needed in the upper coil to exert a force of 3.30 N on the bottom coil

Explanation:

Our Given Parameters include:

Average radius (r) for each parallel coil = 12.5 cm = 12.5 × 10⁻² m

The lower coil turns = 20 turns

The lower coil constant current = 1.30 A

The upper  is suspended 0.314 cm above the lower coil

That indicates the distance = 0.314 cm = 0.314  × 10⁻² m

Current for the upper coil = ???(unknown)

Force (F) = 3.30 N

If we take each coil into cognizance as a long parallel straight wire; then the length of the lower coil can be calculated as:

where:

= number of turns of the lower coil = 20 turns

r = average radius in the lower coil = 12.5 × 10⁻² m

Substituting our values; we have:

From our parameters above:

= constant current in the lower coil = 4.0 A

But the magnitude of the magnetic force (F) = 1 LB

Then the force on the lower coil in regard to the upper coil can be :

F =

Making the varied current in the upper coil the subject of the formula; we have:

where :

Then:

≅ 2539 A

However; the current needed in the upper coil in each turn will be:

amplitude

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