Consider two massless springs connected in series. spring 1 has a spring constant k1, and spring 2 has a spring constant k2. a constant force of magnitude f is being applied to the right. when the two springs are connected in this way, they form a system equivalent to a single spring of spring constant k.

Equivalent spring constant

Explanation: Spring constant, also known as stiffness constant is the amount of load (force) required to make a deformation of unit length in the size of  the spring from its free .

Mathematically given as:

...............(1)

In series the springs are connected back to back consecutively in a single line as shown in figure.

In such a case:

Mathematically represented as:

...........................(2)

∵ From eq. (1) & (2) we have,

              ∵F=-kx, where negative sign denotes that the restoration force acts in the direction opposite to the applied force.

∵The equivalent force is equal on each spring.

We get the relation as:

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the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it