Solveeit Logo
Login

Question

Question: Two identical circular loops of metal wire are lying on a table without touching each other. Loop-A ...

Two identical circular loops of metal wire are lying on a table without touching each other. Loop-A carries a current which increases with time. In response, what will happen in the loop-B?

Explanation

Solution

To solve this problem use Lenz’s law to interpret a relation between the current in the first loop to the second loop. Lenz’s laws states that change of magnetic field with time induce a voltage across a current loop in kept in the magnetic field

Formula used:
The mathematical expression for the induced E.M.F across the loop is given by,
ξ=−dφdt\xi = - \dfrac{{d\varphi }}{{dt}}
Where, ξ\xi is the induced E.M.F across the loop and dφdt\dfrac{{d\varphi }}{{dt}} is the rate of change of a magnetic flux per time.

Complete step by step answer:
We know that Lenz's law states that the current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion. The magnitude of E.M.F induced in a coil is proportional to the rate of change of the magnetic field. The mathematical expression for the induced E.M.F across the loop is given by, ξ=−dφdt\xi = - \dfrac{{d\varphi }}{{dt}} .

Now, here, due to the change in the current flow in the first loop there will be a magnetic field induced to it. Since, the loops are lying horizontal this magnetic field will link flux to the loop –B. Now, from Lenz’s law we know that this change in magnetic field will induce a voltage which will oppose the change in magnetic field means it will repel the flow of current in the loop-A.

So, Loop-A carries a current which increases with time. In response, loop-B is repelled by loop-A vice versa loop-A is repelled by loop-A.

Note: The magnetic flux of through a loop is a given by the dot product of the magnetic field and the surface vector. φ=∮B⃗.ds⃗\varphi = \oint {\vec B.d\vec s} where, B⃗\vec B is the magnetic field of the region and ds⃗d\vec s is the elementary surface vector. If the field lines and the magnetic field are perpendicular to each other linked flux is zero.