Two identical circular loops of metal wire are lying on a table near to each other without touching. Loop A carries a current which increasing with time. In response the loop B......... (a) Is repelled by loop \(\mathrm{A}\) (b) Is attracted by loop \(\mathrm{A}\) (c) rotates about its centre of mass (d) remains stationary

Since loop A carries a current that increases with time, it will create a magnetic field around it. According to Faraday's law of electromagnetic induction, the change in this magnetic field induces an electromotive force (EMF) in loop B. The EMF is given by the equation: \(EMF = -\frac{d\Phi}{dt}\), where \(\Phi\) is the magnetic flux through loop B and \(t\) is time.

Now, we can apply Lenz's law, which states that the direction of the induced current in loop B will be such that it opposes the change in the magnetic field created by loop A. In other words, loop B will generate a magnetic field to oppose the increase in magnetic field due to loop A's increasing current.

As the magnetic field of loop A increases, loop B will experience a force due to the interaction between the magnetic fields of both loops. To determine the nature of this force (attractive or repulsive), we need to consider the direction of the induced current in loop B and its corresponding magnetic field. Since the current induced in loop B is such that it opposes the change in the magnetic field created by loop A, we can conclude that the force acting on loop B will be attractive, as it will try to minimize the rate of change of the magnetic flux. Hence, the correct answer is (b) Loop B is attracted by loop A. Option (a) is incorrect because the force is attractive, not repulsive. Option (c) is incorrect because there is no mention of any external force causing loop B to rotate about its center of mass. Option (d) is incorrect because loop B does not remain stationary; it experiences an attractive force due to the interaction with loop A's magnetic field.