Figure 3 shows a possible device for measuring magnetic fields. A loop carrying

Question

Figure 3 shows a possible device for measuring magnetic fields. A loop carrying a current I is dipped into a region of magnetic field. The loop is suspended from a spring of spring constant k that stretches if the magnetic field points in a certain direction. Here the loop has width l=1 cm, I=1 mA, the spring stretches 0.5 cm, k =4 *10^-4 N / m , and the magnetic field is uniform. What is the magnitude of the field? For the setup to work, is the current I clockwise

http://i64.tinypic.com/35bccir.png

Explanation / Answer

The force on the lower side stretches the string

Force of stretch on the spring = k = 4 x 10-4  x 0.005 = 2 x 10-6 N

This should be equal to the magnetic force on the lower side which is acting downwards

magnetic force = I L x B where Lx B is the cross product between length L and magnetic field B.

Here anyway, since the B and L are perpendicular,

F = I LB = 10-3 x 0.01 x B

2 x 10-6 = 10-3 x 0.01 x B

B = 2 x 10-6 / (  10-3 x 0.01 ) = 0.2 T

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