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A physicist measures the magnetic field at the center of a loop of wire with N...

A physicist measures the magnetic field at the center of a loop of wire with N number of turns (not a solenoid) and current I flowing through it. They then triple the number of coils and half the radius of the coil while keeping the current the same. How does the magnetic field compare in the new situation, B2, compared to the first measurement, B1?
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Answer #1

The magnetic field (B) at the centre of a loop having N number of turns and radius R, carrying a current I is given by the equation,

where is called the permeability of free space. Its value is 4 x 10-7 N/A2

Case (i): When the number of turns of the loop is N and the radius of the loop is R,

Case (ii): When the number of turns of the loop is 3N and the radius of the loop is R/2

Hence we can see that the magnetic field B2 is three times B1.

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