The figure shown depicts the cross section of current carrying ring of wire havi

Question

The figure shown depicts the cross section of current carrying ring of wire having radius of 4 cm A 1-A current flow in the ring in the direction indicated in the drawing. The ring is free to rotate, clockwise or counterclockwise, about an axis normal to the page which passes through its center The ring is connected to a spring with a spring constant of 100 N/m as shown The spring is fixed to a wail at the other end Wien the ring is in the vertical position, the spring is at its natural length. One may assume that the length of the is long enough such that any extension or compression follows Hooke's law. Determine the magnitude of the change in length of the spring when a magnetic field d B = 2 T is along the vertical axes. 1.25 mm 5.0 mm 2.5 mm 6.26 mm

Explanation / Answer

use the equation of magnetic force = Spring force

i.e

i L B = k x

i is current

L is length of the conductor = 2pi r

r is radius

B is magentic field

k is spring constant

x is change of length

so

x = 1* (2*3.14 * 0.04)* 2/(100)

x = 5 mm

option 2 it is

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