Question

The two springs in the figure each have a spring constant of 11 N/m . They are stretched by 0.90 cm when a current passes through the wire.

How big is the current?
Express your answer using two significant figures.
I = ___________A

Answer 1

Spring constant (k) of each spring = 11 N/m

Stretched distance (x) of each spring = 0.90 cm

                                                          = 0.009 m

Here the springs are connected in the parallel combination, so the effective spring consant is

                     k_eff = k₁ + k₂

                           = k + k

                           = 2k

                           = 2(11 N/m)

                           = 22 N/m

Therefore, the force acting on the spring is balanced with force acting on the current carrying wire due to the magnetic field.

Therefore, k_effx = BIL

                      I = (k_effx) / (BL)

                        = [(22 N/m)(0.009 m)] / [(0.50 T)(20 cm)]

                        = [(22 N/m)(0.009 m)] / [(0.50 T)(0.20 m)]

                        = 1.98 A