Question

If a current is passed in a spring it:
A. gets compressed
B. gets expanded
C. oscillates
D. remains unchanged

Answer 1

In this question we have been asked to determine the nature of the spring when some amount of current is passed through it. Now, we know that the loops of the spring can be considered as closely placed parallel connections of coils. Therefore, to answer this question we shall discuss the effect of current flowing through parallel coils.

Complete answer:
We know that the spring can be considered as two parallel wires carrying current as shown in the diagram below.

We know that for a current carrying wire, there will be a magnetic field as shown in the diagram above. At the distance of ‘h’ the magnetic field has magnitude.,
${{B}_{1}}=\dfrac{{{\mu }_{o}}{{I}_{1}}}{2\pi h}$
Now, we know that the second wire carrying current will experience a force say ${{F}_{2}}$due to the magnetic field ${{B}_{1}}$. The force will be given by,
${{F}_{2}}={{I}_{2}}\times l\times {{B}_{1}}\times \dfrac{{{\mu }_{o}}{{I}_{2}}{{I}_{1}}l}{2\pi h}$
Now, from Newton's third law we know that every force will have an equal and opposite reaction. Therefore, the force ${{F}_{1}}$ will act in the opposite direction having the magnitude,
${{F}_{1}}={{I}_{1}}\times l\times {{B}_{2}}\times \dfrac{{{\mu }_{o}}{{I}_{1}}{{I}_{2}}l}{2\pi h}$
This force will create a magnetic field say ${{B}_{2}}$.
${{B}_{2}}=\dfrac{{{\mu }_{o}}{{I}_{2}}}{2\pi h}$.
Now, we can see that both the wires will exert the same magnitude of force but in the opposite direction. As shown in the figure the two wires will attract each other.
Now, we know that the two adjacent loops in the spring are the same as the two wires carrying current. Therefore, the two loops will also attract each other when the current is passed through them. As a result, each loop will attract the other and the spring will get compressed.

Therefore, the correct answer is option A.

Note:
Newtons third law states that to every force applied that will always be an equal and opposite reaction force. The opposite forces in case of the two wires attract each other. A charge that is moving in the magnetic field will experience a force that is perpendicular to the velocity of the particle itself and the magnetic field.